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Problem 1 Consider the matrix Problem 1 Consider the matriz a 2 5 3 11 08...
Problem 8. a) Find the determinant det (A) for the matrix [1 -3 41 A 2 0 -1 1 b) Decide whether the matrix A has an inverse. If the inverse matrix A-1 exists, find its determinant det(A-1).
Problem 4 Reduce the matriz A and find A- A = (1 2 1 1 1 1 1 (3-11) by using row operations (write all corresponding E, matrices) and simultaneously apply these op- erations to the identity matrix to produce its inverse matrix. THIS MEANS: each step in your table has the form (ABE) (where * contains rows operations R R, R R + AR; or R + R), with the initial step (ABLE ] = |A77), the beginning of...
(Has to be done by hand) HW10P1 (12 points) For the following system of equations 3x1 - x2 + 4x3 = -9 -4x, + x2 + 2xy = -4 2x1 + x3 = 0 a. (2 pts) Write the linear system in the format, A x = b. b. (2 pts) Find the determinant of the matrix A by using an expansion along row 1. c. (2 pts) Find the determinant of the matrix A by using an expansion along...
EXERCISE 5.2 1. Evaluate the following determinants: 2. Determine the signs to be attached to the relevant minors in order to get the following cofactors of a determinant: (C13l, IC23i, (C3sl. Canl, and Cu). 6. Find the minors and cofactors of the third row, given EXERCISE 5.3 4. Test whether the following matrices are nonsingular: EXERCISE 5.4 4. Find the inverse of each of the following matrices: 6. Solve the system Ax=d by matrix inversion, where EXERCISE 5.5 1. Use Cramer's rule to solve the following equation systems: 3. Use Cramer's...
3 -5 0 1 0 2 0 0 Consider the matrix A= -1 -1 0 3 1 0 -3 2 Which of the following statements about the determinant of A is true? det(2A) = 2 det A det(-A) = det A O Multiplying any row of Aby -1 does not change det A Interchanging two rows of A does not change det A
Problem 2. (50 points) Suppose that a 4 x 4 matrix A with rows it. 73, 74, and has determinant det A = 1. Find the following determinants: ☺ U2 ü det 604 det det A +50 Note: You can earn partial creat on this problem Problem 1. (50 points) Let Rem -5 -20 -1 -1 - 1 4 16 0 الها (a) Compute dexA Use Cramer's rule to solve the following system 20x -5x -X -4 3 + 16x9...
Find the determinant of the matrix. Expand by cofactors [ 7-11 1-5 10 (a) Row 2 (b) Column 2 284 noints SOLICA
Determinants and linear transformations 4. (a) Let A be the matrix 1 -2 4 1 3 2 11 i) Calculate the determinant of A using cofactor expansion of row 3. (ii) Is A invertible? If so, give the third column of A1 (you do not have to simplify any fractions) (b) Let B be the matrix 0 0 4 0 2 8 0 4 2 1 0 0 0 7 Use row operations to find the determinant of B. Make...
Workout Problems (10 points each) For questions 11-12, consider the following system (x - 5y + 3z = 2. 2x - 3y + 5z = 1. 2y + 5z = 6. 11. Find the determinant of the coefficient matrix, det(A). 12. Solve the system by using Cramer's Rule.
LarPCalc8 8.1.012 45 points 1. Determine the order of the matrix. 47 15 0 -1 0 3 3 6 7 -3 1 O-15 points LarPCalc8 8.1.020. 2. Write the augmented matrix for the system of linear equations. {Sx 4y-2z 24 -21y +8z -3 8x + O-15 points LarPCalc8 8.1.022 My Nete 3. Write the system of linear equations represented by the augmented matrix. (Use the variables x, y, z, and w, if applicable.) 7 -5-4 3 39 8 O-5 points...