
(10 pts) If the determinant of a 5 x 5 matrix A is det (A) = 8, and the matrix B is obtained from A by multiplying the second column by 9, then det (B) =
6. (5 points) Suppose the elementary matrix E is of this form (a) Compute the matrix multiplication EB (b) Compute the determinant of EB using the cofactor expansion along the 1st row of the matrix, and show that the determinant is equal to -det(B) (MUST use the cofactor expansion, no points will be given for other meth- ods.) Hint: Same, don't expand everything out, you will be drown in a sea of bij, you should look at the cofactor expansion...
Problem 1 Consider the matrix Problem 1 Consider the matriz a 2 5 3 11 08 a Find the cofactors C11,C2,C3 of A. b Find the determinant of 1, det(A) [ 2 4 61 Problem 2 Consider the matriz A=008 | 2 5 3 a Use the ero's to put A in upper triangular form 5 Pinul the determinant of A. (A) by keeping track of the row operations in part a and the properties of determinant Problem 3 Consider...
Please answer this using matrices quick thanks
1. Let A be a 3 x 3 matrix with det (A) 4, and suppose the matrix B is obtained from A by performing the following elementary row/column operations to A: -a Ra+ Rs For what value(s) of a does det(B)-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...
11. (1 pt) A and B are nxn matrices. Check the true statements below: A. The determinant of A is the product of the pivots in any echelon form U of A, multiplied by (-1)', where r is the number of row interchanges made during row reduction from A to U. B. If the columns of A are linearly dependent, then detA=0. • C. Adding a multiple of one row to another does not affect the determinant of a matrix....
(3 points) Let A be a 4 x 4 matrix with det(A) = 8. 1. If the matrix B is obtained from mes the second row to the first, then det(B) = 2. If the matrix C is obtained from A by swapping the first and second rows , then det(C) = 3. If the matrix D is obtained from A by multiplying the first row by 5, then det(D) =
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 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)
1. CP1 (20 pts) Consider the system of linear equations X1 + x2 + x3 = 1 X1 - x2 + x3 = 3 - X1 + x2 + x3 = -1 a) (3 pts) Provide the Augmented matrix A for this system. b) (9 pts) Find the Row-Echelon Form (AREF) of the Augmented matrix. c) (2 pts) How many solutions does the system have? d) (6 pts) Based on the steps in part b), express Aref as a product...