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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Evaluate the given determinants by expansion by minors. -2 1 4 2432 4 1 3 3-2 3-2 3 1 -2 -2 15
Show that AI = IA = A. A = 18 -2 2
Use matrices A, B, C, and D to find the indicated matrices. If the operations cannot be performed, explain why.2A + B A || 6-3 4 -5 B 1) -1 4 -7 2 -6 11 3 12 -9 -6 D= 79 -6 -4 0 8 16000
Solve the given systems of equations by using the inverse of the coefficient matrix. Use a calculator to perform the necessary matrix operations and display the results and the check. See Example
Evaluate the given determinants by expansion by minors. 1 0 0 1 1 -1 1 102 2 -1 -2 1 2 0 02 1 10-1 -2 0-1 2
Perform the indicated matrix multiplication. 2 - 1 -2 1 | 1 -1 2-2
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them. 2x - 4y = 7 3x + 5y = -6 9x - 7y = 15
Find the inverse of each of the given matrices by transforming the identity matrix, as in Examples 2–4.Data from Example 4Find the inverse of the matrixTherefore, the required inverse matrix
Solve the given systems of equations by using the inverse of the coefficient matrix. Use a calculator to perform the necessary matrix operations and display the results and the check. See Example
Show that AI = IA = A. A = -15 28 -5 64
Use matrices A, B, C, and D to find the indicated matrices. If the operations cannot be performed, explain why.C − D A || 6-3 4 -5 B 1) -1 4 -7 2 -6 11 3 12 -9 -6 D= 79 -6 -4 0 8 16000
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them. 4x - y = 5 8x + 8y = 12 6x - 4y = 7 2x + y = 4
Perform the indicated matrix multiplications. 6-4 10 2 0-4 3 7 -1 6 4 0 1 3 -2 5 9 10
Solve the given systems of equations by using the inverse of the coefficient matrix. Use a calculator to perform the necessary matrix operations and display the results and the check. See Example
Evaluate the given determinants by expansion by minors. -1 3 5 0 17 5 -2 -1 0 3 3 -3 6 2 - 0-5 3-2 0 2 -1 2 1-4
Use matrices A, B, C, and D to find the indicated matrices. If the operations cannot be performed, explain why.2C + D A || 6-3 4 -5 B 1) -1 4 -7 2 -6 11 3 12 -9 -6 D= 79 -6 -4 0 8 16000
Solve the given systems of equations by determinants. Evaluate by expansion by minors. 2x + 2t = 0 -1 3x + y + z = 2yz + 3t = 1 2z3t = 1
Use matrices A, B, C, and D to find the indicated matrices. If the operations cannot be performed, explain why.−2C + D A || 6-3 4 -5 B 1) -1 4 -7 2 -6 11 3 12 -9 -6 D= 79 -6 -4 0 8 16000
Find the inverse of each of the given matrices by using a calculator. -2 8 -1 6
Show that AI = IA = A. A = 386 3 9-15 0 6-12 8 4 24
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them. 6x + 10y = -4 24x 18y = 13 15x 33y = 19 6x + 68y = -33
Perform the indicated matrix multiplication. 0 0.6 0.2 0.0 0.4 -0.1 0.1 0.4 0.5 0.5 0.1 0.0
Solve the given systems of equations by using the inverse of the coefficient matrix. Use a calculator to perform the necessary matrix operations and display the results and the check. See Example
Find the inverse of each of the given matrices by using a calculator. 20 - 12 -45 24
Show that AI = IA = A. A = -1 4 2 2 0 -3 1 13
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them. x + 3y - z = 1 3x - y + 4z = 4 -2x + 2y + 3z = 17 3x + 7y + 5z = 23
Solve the given systems of equations by determinants. Evaluate by expansion by minors. 2x + y + z = 4 2y2zt = 3 3y 3z + 2t 1 = 6xy + t = 0
Use matrices A, B, C, and D to find the indicated matrices. If the operations cannot be performed, explain why.2B − D A || 6-3 4 -5 B 1) -1 4 -7 2 -6 11 3 12 -9 -6 D= 79 -6 -4 0 8 16000
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them. 4x8y8z = 12 10x + 5y + 15z = 20 -6x - 3y 3z = 15 3x + 3y2z = 2
Determine whether or not B = A−1. 5 -2 12 ^-| -2 -1 -1 2 3] A = B = 25
Find the inverse of each of the given matrices by using a calculator. 13 2 -2 -5 -1 24 4 0
Find the inverses of the given matrices. Check each by using a calculator. 2-5 2-4
Perform the indicated matrix multiplication. 0-1 8 1 7 -2 6 4 -1 5 -1 7 1 0 104 4 1 -2 3 0 15 1 1
Solve the given systems of equations by using the inverse of the coefficient matrix. Use a calculator to perform the necessary matrix operations and display the results and the check. See Example 4.u
Solve the given systems of equations by using the inverse of the coefficient matrix. Use a calculator to perform the necessary matrix operations and display the results and the check. See Example
Solve the given systems of equations by determinants. Evaluate by expansion by minors. x + 2y z = 6 - y2z3t 3x - 2y + t = 2 2x+y+z-t=0 = -5
Use matrices A, B, C, and D to find the indicated matrices. If the operations cannot be performed, explain why.D − 4C A || 6-3 4 -5 B 1) -1 4 -7 2 -6 11 3 12 -9 -6 D= 79 -6 -4 0 8 16000
Determine whether or not B = A−1. A 3-4 5-7 B = 7 -4 5-2
Find the inverse of each of the given matrices by using a calculator. 13 -1-4-2 9 20 4 4 ੧.
Use matrices A, B, C, and D to find the indicated matrices. If the operations cannot be performed, explain why.−C − 2D A || 6-3 4 -5 B 1) -1 4 -7 2 -6 11 3 12 -9 -6 D= 79 -6 -4 0 8 16000
Find the inverses of the given matrices. Check each by using a calculator. -5 -30 10 50
Solve the given systems of equations by using the inverse of the coefficient matrix. Use a calculator to perform the necessary matrix operations and display the results and the check. See Example
Solve the given systems of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them. 2x y2z - t = 4 - 4x + 2y + 3z + 2t -2xy + 4z = -2 = 3
Solve the given systems of equations by determinants. Evaluate by expansion by minors. 2p+ 3r + s = 4 p2r3s 3p+r+s 5t = 3 - -p+2r + s + 3t = 2 + 4t = -1
Solve the given system of equations by using the rref feature on a calculator. 7x + 5y 3z = 16 3x - 5y + 2z = -8 5x + 3y 7z = 0 -
Solve the given systems of equations by determinants. Evaluate by using a calculator. 2x + y + z = 2 3yz + 2t = 4 y + 2z+ t = 0 3x + 2z = 4
Find the inverse of each of the given matrices by using a calculator. 24 0 3 4-2 -1 12
Determine whether or not B = A−1. A = 1-2 3 لا لا 2-5 7 -1 3-5 B = 4 -1 3-2 1-1 -1 1 -
Solve the given systems of equations by using the inverse of the coefficient matrix. Use a calculator to perform the necessary matrix operations and display the results and the check. See Example
Determine whether or not B = A−1. A 1 - 1 3-4 384 3 -2 3-4 B= 8-5 -4 4-2 -1 1 T 1
Use matrices A, B, C, and D to find the indicated matrices. If the operations cannot be performed, explain why.B − 3A A || 6-3 4 -5 B 1) -1 4 -7 2 -6 11 3 12 -9 -6 D= 79 -6 -4 0 8 16000
Find the inverses of the given matrices. Check each by using a calculator. -0.8 -0.1 0.4 -0.7
Solve the given systems of equations by determinants. Evaluate by using a calculator. 6x + 3y + 3z = 0 x = y + 2t = 2 2y+z+ 4t = 2 5x + 2z+ 2t = 4
Find the inverse of each of the given matrices by using a calculator. 10 -2 20 -5 30 4-5 5 с 5
Find the inverses of the given matrices. Check each by using a calculator. 50 -12 42 -80
Solve the given system of equations by using the rref feature on a calculator. x + y + z = 6 2y + 5z = -4 2x + 5y z = 27 -
Use matrices A, B, C, and D to find the indicated matrices. If the operations cannot be performed, explain why.2A − 1/3B A || 6-3 4 -5 B 1) -1 4 -7 2 -6 11 3 12 -9 -6 D= 79 -6 -4 0 8 16000
Solve the given systems of equations by using the inverse of the coefficient matrix. Use a calculator to perform the necessary matrix operations and display the results and the check. See Example
Solve the given systems of equations by determinants. Evaluate by using a calculator. D + E + 2F = 1 2D E + G = -2 D-E-F- 2G = 4 2D E2F - G = 0 -
Find the inverse of each of the given matrices by using a calculator. 1-2 1-2 0 -2 10 2 -3 1 - 1 3-2 1 3
Find the indicated matrices using a calculator.3A A = c = C 6-3 4 -5 B = -1 4 -7 2 -6 11 3 -9 D = 12 -6 79-6 -4 0 8
Solve the given system of equations by using the rref feature on a calculator. -2r + 3t 5u = 1 -4r + s-2t + u = 0 r4s + 2t +u = 4 -5r 3s + 8u = 0
Find the inverse of each of the given matrices by using a calculator. 12.5 -2.6 1.2 7.6 -4.6 10.0 -4.7 -6.8 5.7 -3.7 7.3 11.0 8.8 6.8 4.7 14.0
Find the inverses of the given matrices. Check each by using a calculator. 1 1 -2 -2 1 3 4 -1 0
Solve the given systems of equations by using the inverse of the coefficient matrix. Use a calculator to perform the necessary matrix operations and display the results and the check. See Example
Determine by matrix multiplication whether or not A is the proper matrix of solution values.
Determine by matrix multiplication whether or not A is the proper matrix of solution values. 4x + y = -5 3x + 4y = 8 A = -2 3
Solve the given system of equations by using the rref feature on a calculator. 2x + 5y9z+ 3w = 151 5x + 6y4z + 2w = 103 3x - 4y + 2z + 7w 16 11x + 7y + 4z - 8w = -32
Solve the given systems of equations by determinants. Evaluate by using a calculator. 3x + y + t = 0 3z + 2t = 8 6x + 2y + 2z + t = 3 3.xyz-t = 0
Find the indicated matrices using a calculator.−2C A = c = C 6-3 4 -5 B = -1 4 -7 2 -6 11 3 -9 D = 12 -6 79-6 -4 0 8
Find the inverses of the given matrices. Check each by using a calculator. -1 2 1 -1 2 30 4 1
For the following system of equations, solve for x2 and y using the matrix methods of this section, and then solve for x and y.x2 + y = 22x2 – y = 10
Find the BA−1. B = 8 -2 3 4 5 2 -3 -1 0 -2 1 04
Determine by matrix multiplication whether or not A is the proper matrix of solution values. 3x + y + 2z = 1 x - 3y + 4z = -3 A = 2x + 2y + z = 1 2 1
Make the indicated changes in the determinant at the right, and then solve the indicated problem. Assume the elements are nonzero, unless otherwise specified.Evaluate the determinant if a = c, d = f
Find the indicated matrices using a calculator.C + 3D A = c = C 6-3 4 -5 B = -1 4 -7 2 -6 11 3 -9 D = 12 -6 79-6 -4 0 8
Find the inverses of the given matrices. Check each by using a calculator. 2-4 -6 3 5 1-1 4 -2
Find the BA−1. B = 8 -2 3 4 5 2 -3 -1 0 -2 1 04
Solve the system a1x + b1y = c1, a2x + b2y = c2 and show that the result is the same as that obtained using Cramer’s rule as in Section 5.4.
For the following system of equations, solve for x2 and y2 using the matrix methods of this section, and then solve for x and y.x2 – y2 = 8x2 + y2 =10
Determine by matrix multiplication whether or not A is the proper matrix of solution values.
Solve the system x + 2y = 6, 2x + ay = 4 and show that the solution depends on the value of a. What value of a does the solution show may not be used?
A smaller of two cubical boxes is centered on the larger box, and they are taped together with a wide adhesive that just goes around both boxes (see Fig. 14.22). If the edge of the larger box is 1.00
Solve the given equations algebraically and check the solutions with a calculator.x3 − 2x3/2 − 48 = 0
Solve the given equations without using a calculator.x4 − 11x2 − 12x + 4 = 0
Find the remaining roots of the given equations using synthetic division, given the roots indicated.3x³ + 15x² + 27x + 15 = 0 (r1 = −2 + j)
Use the factor theorem to determine whether or not the second expression is a factor of the first.9v3 + 6v2 + 4v + 2; 3v + 1
Find the remainder using the remainder theorem. Do not use synthetic division.(4x4 − x3 + 5x − 7) ÷ (x − 5)
Solve the given equations without using a calculator.8x4 − 32x3 − x + 4 = 0
Find the remaining roots of the given equations using synthetic division, given the roots indicated.t³ − 7t² + 17t − 15 = 0 (r1 = 2 + j)
Use synthetic division to perform the indicated divisions.(x3 + 4x2 + 5x + 1) ÷ (x − 1)
Find the remainder using the remainder theorem. Do not use synthetic division.(2x4 − 7x3 − x2 + 8) ÷ (x + 1)
Solve the given equations without using a calculator.5n4 − 2n3 + 40n − 16 = 0
Find the remaining roots of the given equations using synthetic division, given the roots indicated.x4 − 2x3 − 20x² − 8x − 96= 0 (r1 = 6, r2 = −4)
Use synthetic division to perform the indicated divisions.(3x3 − 2x2 + 7) ÷ (x − 3)
Find the remainder using the remainder theorem. Do not use synthetic division.(3n4 − 13n2 + 10n − 10) ÷ (n + 4)
Solve the given equations without using a calculator.8n4 − 34n2 + 28n − 6 = 0
Find the remaining roots of the given equations using synthetic division, given the roots indicated.2x4 − 19x3 + 39x2 + 35x − 25 = 0 (5 is a double root)
Use synthetic division to perform the indicated divisions.(2x3 − 3x2 − 4x + 3) ÷ (x + 2)
Find the remainder using the remainder theorem. Do not use synthetic division.(x5 − 3x3 + 5x2 − 10x + 6) ÷ (x + 2)

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