[5] (c) Let A and B be two 3x3 matrices, and let X = Suppose further...
Let A and B be 3x3 matrices, with det A=9 and det B = - 6. Use properties of determinants to complete parts (a) through (e) below. a. Compute det AB. det AB = (Type an integer or a fraction.) b. Compute det 5A. det 5A = (Type an integer or a fraction.) c. Compute det BT. det BT = (Type an integer or a fraction.) d. Compute det A-7. - 1 det A (Type an integer or a simplified...
1. Write TkuE or FaLsE for each of the following, and give a brief (specific!) justification. (i) Let A and B be square n x n nonsingular matrices. Then (AB) A- B-1 (ii) A homogeneous system of linear equations can have a unique solution. i) Suppose A is a nonsingular matrix. Then det (A-)- det(A) (iv) Diagonal matrices are always orthogonal. (v) If T and S are both linear transformations, then the linear transformation described by TS is the same...
4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det (A?)? (d) (4 points) What is det(A-?)? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of AT are linearly independent. and 2 6. (6 points) Let...
4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(AT)? (d) (4 points) What is det(A-')? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of A™ are linearly independent. and t = [ ] 6. (6...
4. Let A and B be 4 x 4 matrices. Suppose det A= 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(AT)? (d) (4 points) What is det(A-1)? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of AT are linearly independent. [2] and us 6. (6 points) Let vi...
L. Answer True or False. Justify your answer (a) Every linear system consisting of 2 equations in 3 unknowns has infinitely many solutions (b) If A. B are n × n nonsingular matrices and AB BA, then (e) If A is an n x n matrix, with ( +A) I-A, then A O (d) If A, B two 2 x 2 symmetric matrices, then AB is also symmetric. (e) If A. B are any square matrices, then (A+ B)(A-B)-A2-B2 2....
SOLVE BOTH 4 and 5!! 4. Let A and B be two nxn matrices. Suppose that AB is invertible. Show that the system Ar 0 has only the trivial solution 5. Given that B and D are invertible matrices of orders n and p respectively, and A = Find A by writing A as a suitably partitioned matrix
Two augmented matrices for two linear systems in the variables x, y, and z are given below. The augmented matrices are in reduced row-echelon form. For each system, choose the best description of its solution If applicable, give the solution. 8 (loo 8 0106 001 -4 The system has no solution. The system has a unique solution (x, y, z) = 0.00 ? The system has infinitely many solutions. . (x... CD 00.-) (b) (1 0-1 1 2 01 15...
Matrix Methods/Linear Algebra: Please show all work and justify the answer! 4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(A”)? (d) (4 points) What is det(A-")? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of...
[4 points Suppose A, B, and Care 5 x 5 matrices with det(A) = -2, det(B) = 10 and the columns of C are linearly dependent. Find the following or state that there is not enough information: (a) det(10B-) (b) det(AB) (c) det(CA+CB)