1. [-/2 Points] DETAILS LARLINALGS 1.2.019.EP. MY NOTES ASK Y! Consider the following matrix. 1 0 0 o = O 0 1 0 o o O Determine which conditions are satisfied by the matrix. (Select all that apply.) [J Any rows consisting entirely of zeros occur at the bottom of the matrix. [J For each row that does not consist entirely of zeros, the first nonzero entry is 1. [J For two successive (nonzero) rows, the leading nonzero value in the higher row is farther to the left than the leading nonzero value in the lower row. [[J Each column that has a leading 1 has solely zeros elsewhere. Determine whether the matrix is in row-echelon form. If it is, determine whether it is also in reduced row-echelon form. (Select all that apply.) [J row-echelon form [J reduced row-echelon form [J neither 2. [-/5 Points] DETAILS I LARLINALGS 1.2.023.SBS. MY NOTES ASK YOUR TE Determine whether the matrix is in row-echelon form. If it is, determine whether it is also in reduced row-echelon form. 00100 00010 00010 STEP 1: Check rows consisting entirely of zeros. Do all rows (if any) consisting entirely of zeros occur at the bottom of the matrix? O Yes O No O There are no rows consisting entirely of zeros. STEP 2: Check the first nonzero entry of each row. Does each row that does not consist entirely of zeros have the first nonzero entry equal to 1? O Yes O No O There are no rows that do not consist entirely of zeros. STEP 3: Check successive nonzero rows. If %lch nonzero row has a leading 1, is the leading 1 in the higher row farther to the left of the leading 1 in the lower row for each pair of successive rows? Yes O No O There exists at least one row which does not have a leading 1. STEP 4: Check the columns with leading ones. Does every column with a leading 1 have zeros in every position above and below its leading 1? O Yes QO No STEP 5: Determine the form of the matrix. (Select all that apply.) [J row-echelon form [ reduced row-echelon form O neither 3. [-/2 Points] DETAILS LARLINALG8 1.2.040. MY NOT Use a software program or a graphing utility to solve the system of linear equations. (If there is no solution, enter NO SOLUTION. If the system has in terms of the parameter t.) X1 + X2 - 2X3 + 3x4 + 2X5 = 16 3x, + 3X, - X3 + X4+ X5 = 15 2x, + 2x2 - X3 + X4 - 2x5 = 8 4x, + 4X2+ X3 - 3x5 = 17 8x, + 5X, - 2X3 - X4 + 2X5 = 23 (X 1, X21X31 X41 X5) = Need Help? Read It Submit Answer 4. [-/3 Points] DETAILS LARLINALG8 1.2.041. MY NOT Use a software program or a graphing utility to solve the system of linear equations. (If there is no solution, enter NO SOLUTION. If the system has X3, and x in terms of t.) X1 - X2 + 2X3 + 2X4 + 6X5 = 11 3x1 - 2X, + 4X3 + 4X4 + 12x5 = 23 X2 - X3 - X4 - 3X5 = -6 2x, - 2X, + 4X3 + 5X + 15X5 = 23 2x1 - 2x, + 4X3 + 4x + 13x5 = 24 (X1, X21 X31 X41 X5) =5. [-/6 Points] DETAILS LARLINALG8 1.2.049. Consider the following matrix. Assume that the matrix is the augmented matrix of a system of linear equations. (a) Determine the number of equations and the number of variables. equations variables (b) Find the value(s) of k such that the system is consistent. OK = O k = O all real k * - O all real k # _ O all real k Assume that the matrix is the coefficient matrix of a homogeneous system of linear equations. (a) Determine the number of equations and the number of variables. equations variables (b) Find the value(s) of k such that the system is consistent. OK = OK = . O all real k # O all real k #_6. [-/1 Points] DETAILS LARLINALG8 1.2.054. Assume the system below has a unique solution. allX1 + @12*2 + @13*3 = b1 Equation 1 a21X1 + azz*2 + 23*3 = b2 Equation 2 a31X1 + 232*2 + 233*3 = b3 Equation 3 Does the system composed of Equations 1 and 2 have a unique solution, no solution, or infinitely many solutions? O unique solution O no solution O infinitely many solutions Need Help? Read It Submit Answer 7. [-/1 Points] DETAILS LARLINALG8 1.2.056. Find the reduced row-echelon matrix that is row-equivalent to the given matrix. 1 2 3 4 5 6 8 9