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mathematics
basic technical mathematics
Basic Technical Mathematics 12th Edition Allyn J. Washington, Richard Evans - Solutions
Solve the given equations without using a calculator.12x4 + 44x3 + 21x2 − 11x = 6
Find the remaining roots of the given equations using synthetic division, given the roots indicated.4n4 + 28n3 + 61n2 + 42n + 9 = 0 (−3 is a double root)
Use synthetic division to perform the indicated divisions.(3D3 + 8D2 − 16) ÷ (D + 4)
Find the remainder using the remainder theorem. Do not use synthetic division.(3x4 − 12x3 − 60x + 4) ÷ (x − 0.5)
Solve the given equations without using a calculator.9x4 − 3x3 + 34x2 − 12x = 8
Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division.x5 − 2x4 + 3x3 − 6x2 − 4x + 8, x − 1
Find the remaining roots of the given equations using synthetic division, given the roots indicated.6x4 + 5x3 −15x2 + 4 = 0 (r1 = −1/2, r2 = 2/3)
Use synthetic division to perform the indicated divisions.(x4 + 3x3 − 20x2 − 2x + 56) ÷ (x + 6)
Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division.8x3 + 2x2 − 32x − 8, x − 2
Solve the given equations without using a calculator.D5 + D4 − 9D3 − 5D2 + 16D + 12 = 0
Find the remaining roots of the given equations using synthetic division, given the roots indicated.6x4 − 5x³ − 14x² + 14x − 3 = 0 (r1 = 1/3, r2 = 3/2)
Use synthetic division to perform the indicated divisions.(x4 − 6x3 + x − 8) ÷ (x − 3)
Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division.3x3 + 14x2 + 7x − 4, x + 4
Solve the given equations without using a calculator.x6 − x4 − 14x2 + 24 = 0
Find the remaining roots of the given equations using synthetic division, given the roots indicated.2x4 − x³ − 4x² + 10x − 4 = 0 (r1 = 1 + j)
Use synthetic division to perform the indicated divisions.(2m5 − 48m3 + m2 − 9) ÷ (m − 5)
Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division.3V4 − 7V3 + V + 8, V − 2
Solve the given equations without using a calculator.4x5 − 24x4 + 49x3 − 38x2 + 12x − 8 = 0
Find the remaining roots of the given equations using synthetic division, given the roots indicated.s4 − 8s3 − 72s − 81 = 0 (r1 = 3j)
Use synthetic division to perform the indicated divisions.(x6 + 63x3 + 5x2 − 9x − 8) ÷ (x + 4)
Solve the given equations without using a calculator.2x5 + 5x4 − 4x3 − 19x2 − 16x = 4
Use a calculator to solve the given equations to the nearest 0.01.2x3 − 8x + 3 = 0
Find the remaining roots of the given equations using synthetic division, given the roots indicated.x5 − 3x4 + 4x3 − 4x2 + 3x − 1 = 0 (1 is a triple root)
Use synthetic division to determine whether or not the given numbers are zeros of the given functions.y3 + 4y2 − 9; −3
Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division.x51 − 2x − 1, x + 1
Use a calculator to solve the given equations to the nearest 0.01.2x4 − 15x2 − 7x + 3 = 0
Find the remaining roots of the given equations using synthetic division, given the roots indicated.12x5 − 7x4 + 41x³ − 26x² −28x + 8 = 0(r1 = 1, r2 = 1/4, r3= − 2/3)
Use synthetic division to determine whether or not the given numbers are zeros of the given functions.8y4 − 32y3 − y + 4; 4
Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division.x7 − 128−1, x + 2−1
Find k such that x − 1 is a factor of x3 − 4x2 − kx + 2.
Use a calculator to solve the given equations to the nearest 0.01.2x5 − 3x4 + 8x3 − 4x2 − 4x + 2 = 0
Perform the indicated divisions by synthetic division.(x3 + 2x2 − x − 2) ÷ (x − 1)
Use synthetic division to determine whether or not the given numbers are zeros of the given functions.2x4 − x³ + 2x² + x − 1; −1, 1/2
Use a calculator to solve the given equations to the nearest 0.01.8x4 + 36x3 + 35x2 − 4x − 4 = 0
Find the remaining roots of the given equations using synthetic division, given the roots indicated.P5 − 3P4 − P + 3 = 0 (r1 = 3, r2 = j)
Evaluate the following determinant by expansion by minors. 2 -4 -3 -3 لا لا لا 6 5-15 2
Use the given value of the determinant at the right and the properties of this section to evaluate the following determinants. 2-3 1 1 -3 -4 1 3 -2 40
In Example 2, change the −2 in the first row to 0 and then find the determinant.Data from Example 2In evaluating the following determinant, note that the third column has two zeros. This means that expanding by the third column will require less numerical work. Therefore,As we noted in Chapter 5,
In Example 5(a), interchange the second and third columns of the second matrix and then add the matrices.Data from Example 5(a) 8 1-59 0-2 3 7 + 3 460 6-2 65 = = 8+ (-3) 0+6 5 1+ 4 −2+(-2) 51 -4 9 12 -5+6 9+0 3+6 7+5
In Example 2, interchange columns 1 and 2 in matrix A and then do the multiplication.Data from Example 2The product of two matrices below may be formed because the first matrix has four columns and the second matrix has four rows. The matrix is formed as shown. -19 3 -2 1 1 20-7 6-2 1
In Example 1, change the 18 to 19 and then solve the system of equations.Data from Example 1Use matrices to solve the system of equationsThe matrices for Eq. (16.7), and the matrix equation areBy either of the methods of the previous section, we can determine the inverse of matrix A to beWe now
In Example 2, interchange the two equations and then solve the system with the equations in this order.Data from Example 2Solve the following system of equations using Gaussian elimination:The steps are given below, with the necessary row operations shown in red:To find the value of x, we
In Example 3, change the element −3 to −2 and then find the inverse using the same method.Data from Example 3Find the inverse of the matrixTherefore,which can be checked by multiplication. -3 6 4 5
In Example 5, in A change −2 to 2 and −3 to 3, in B change 2 to −2 and 3 to −3, and then do the multiplications.Data from Example 5For the given matrices A and B, show that AB = BA = I, and therefore that B = A−1.Forming the products AB and BA, we have the following:Since AB = I and BA =
In Example 5, change the third equation of the second system to 5x + 3y = 11.Data from Example 5Solve the following systems of equations by Gaussian elimination. The solutions are shown at the left. We note that each system has three equations and two unknowns. In the solution of the first system,
An open container (no top) is to be made from a square piece of sheet metal, 20.0 cm on a side, by cutting equal squares from the corners and bending up the sides. Find the side of each cut-out square such that the volume is a maximum (see Exercise 69).Data from Exercises 69The entrance to a garden
Evaluate each determinant by inspection. Observation will allow evaluation by using the properties of this section. له 2 0 424 23 ۶۶۶۶ دن ان در 0 -
Perform the indicated multiplication. 0-1 -1 2 4 11 2 1 3 1 6 -1 2 1
Determine the value of the literal numbers in each of the given matrix equalities. If the matrices cannot be equal, explain why. X 2y r/4 -s Z -S-St -2 10 -9 12 -4 5
Determine each of the following as being either true or false. If it is false, explain the reason why.After using two steps of the Gaussian elimination method for solving the systemwe would have 2x + 3y = 3x + 2y = 4 1¹
Find the inverse of each of the given matrices by the method of Example 1 of this section.Data from Example 1Find the inverse of the matrixFirst, we interchange the elements on the principal diagonal and change the signs of the off-diagonal elements. This gives us the matrix.Now, we find the
Evaluate each determinant by inspection. Observation will allow evaluation by using the properties of this section. -12 -24 -24 15 12 32 32 -35 -22 18 18 18 44 0 0 -26
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them.4x – 3y = 2–2x + 4y = 3
Determine the value of the literal numbers in each of the given matrix equalities. If the matrices cannot be equal, explain why. [ a + bj 2c-dj 3e + fj] = [5j a + 6 3b + c ] (j = √-1)
Determine the values of the literal numbers. 4a a - b 8 5
Find the inverse of each of the given matrices by the method of Example 1 of this section.Data from Example 1Find the inverse of the matrixFirst, we interchange the elements on the principal diagonal and change the signs of the off-diagonal elements. This gives us the matrix.Now, we find the
Solve the given systems of equations by using the inverse of the coefficient matrix.2x + 4y = −9 (13)−x − y = 2
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them.–3x + 2y = 44x + y = –5
Determine the value of the literal numbers in each of the given matrix equalities. If the matrices cannot be equal, explain why. C + D D - 2E ЗЕ 3 2 6
Perform the indicated multiplication. -8 -6 ات - 24 2-3 ليا الا ا 8
Solve by using the inverse of the coefficient matrix.2z − 3y = 11x + 2y = 2
Find the inverse of each of the given matrices by the method of Example 1 of this section.Data from Example 1Find the inverse of the matrixFirst, we interchange the elements on the principal diagonal and change the signs of the off-diagonal elements. This gives us the matrix.Now, we find the
Use the given value of the determinant at the right and the properties of this section to evaluate the following determinants. 2-3 1 1 -3 -4 1 3 -2 40
Determine the values of the literal numbers. x - y 2x + 2z 4y + z 1 3 -1 نیا
Solve the given systems of equations by using the inverse of the coefficient matrix.x − 3y − 2z = −8 (17)−2x + 7y + 3z = 19x − y − 3z = −3
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them.2x – 3y + z = 46y – 4x – 2z = 9
Determine the value of the literal numbers in each of the given matrix equalities. If the matrices cannot be equal, explain why. 2x - 3y x + 4y 13 |-(1)
Perform the indicated multiplication. 13105 -1 T의 -5 12 25
Determine the values of the literal numbers. 2x Зу x+a y + b 2z c-z || 4 7 -9 8 -4 2
Solve the given systems of equations by using the inverse of the coefficient matrix.x + 3y + 2z = 5 (19)−2x − 5y − z = −12x + 4y = −2
Find the inverse of each of the given matrices by the method of Example 1 of this section.Data from Example 1Find the inverse of the matrixFirst, we interchange the elements on the principal diagonal and change the signs of the off-diagonal elements. This gives us the matrix.Now, we find the
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them.3s + 4t – u = – 52u – 6s – 8t = 10
Use the given value of the determinant at the right and the properties of this section to evaluate the following determinants. 2-3 1 1 -3 -4 1 3 -2 40
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them. x + 3y + 3z: = -3 2x + 2y + z = −5 -5 -2xy + 4z = 6
Determine the values of the literal numbers. a + bj aj b b - aj || 6j 2d 2cj ej2 (j = √-1)
Solve the given systems of equations by using the inverse of the coefficient matrix.2x − 3y = 34x − 5y = 4
Determine the value of the literal numbers in each of the given matrix equalities. If the matrices cannot be equal, explain why. x -3x+y y + z y-t x-z x + 1 5 3 4 -1 نیا
Solve the following system of equations by using the inverse of the coefficient matrix. Use a calculator to perform the necessary matrix operations and display the result and check. Write down the display shown in the window with the solutions.7x − 2y + z = 62x + 3y − 4z = 64x − 5y + 2z = 10
For what value of k is x + 1 a factor of f(x) = 3x4 + 3x3 + 2x2 + kx − 4?
Find rational values of a such that (x − a) will divide into x3 − 13x + 3 with a remainder of −9.
For what value of k is x − 2 a factor of f(x) = 2x3 + kx2 − x + 14?
If a calculator shows a real root, how many nonreal complex roots are possible for a sixth-degree polynomial equation f(x) = 0?
By division, show that x2 + 2 is a factor of f(x) = 3x3 − x2 + 6x − 2. May we therefore conclude that f(−2) = 0? Explain.
What are the possible combinations of real and nonreal complex zeros (double roots count as two, etc.) of a fourth-degree polynomial?
Use synthetic division to determine whether or not the given numbers are zeros of the given functions.85x3 + 348x2 − 263x + 120; −4.8
Perform the indicated multiplication. 9 1 3 02 7 40 -15 20
Determine the value of the literal numbers in each of the given matrix equalities. If the matrices cannot be equal, explain why. X x + y 2 25
Evaluate each determinant by inspection. Observation will allow evaluation by using the properties of this section. -3 0 0 10 -9 -1 0 0 -5
Find the inverse of each of the given matrices by the method of Example 1 of this section.Data from Example 1Find the inverse of the matrixFirst, we interchange the elements on the principal diagonal and change the signs of the off-diagonal elements. This gives us the matrix.Now, we find the
Determine whether or not B = A−1. A = 2 -5 -2 B = -2 5 - 1 2
Determine each of the following as being either true or false. If it is false, explain the reason why.is the matrix solution of 2-1 5 -3 3 -1 [B-E -6
Perform the indicated multiplication. 4 1 - 46 6 - 3/4 8 -4 09
Find the inverse of each of the given matrices by the method of Example 1 of this section.Data from Example 1Find the inverse of the matrixFirst, we interchange the elements on the principal diagonal and change the signs of the off-diagonal elements. This gives us the matrix.Now, we find the
Solve the given systems of equations by using the inverse of the coefficient matrix.x + 2y = 7 (11)2x + 5y = 11
Determine the value of the literal numbers in each of the given matrix equalities. If the matrices cannot be equal, explain why. ab -3 1:8-11위 cd 4 7
For matrices C and D, find CD and DC, if possible. C = 104 2-2 1 32 - 1 D = 2-2 4-5 6 1
Determine each of the following as being either true or false. If it is false, explain the reason why. 3 1 2-2 3 012 -2 3 12 1: - 21 2
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them.2x + y = 15x + 2y = 1
Evaluate each determinant by inspection. Observation will allow evaluation by using the properties of this section. 10 0 0 -5 8 3-8 0 -3
Solve the given systems of equations by using the inverse of the coefficient matrix.−x + 5y = 4 (5)4x + 10y = −4
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