Initially I have given all the formulae to calculate determinants.
Solution of Problem No. 4
Solution of Problem No. 5
Solution of Problem No. 6
Find ATA and AAT. A = -1 1 0 2 24 (a) AA E (b) AAT Which of the products are symmetric? (Select all that apply.) SATA LAAT
Find ATA and AAT for the following matrix. 4-1-4-6 31 2 -5 4 AAT = What do you observe? This answer has not been graded yet.
three seperate questions multiple choice
13 and B= Find A -B. 2 . [4:1 Let A= -1 6 2 6 7 177 15 12 1 5 5 30 1 5 3 30 7 17 15 36 Let A and B be 3 x 3 matrices with det(A) = 2 and det(B) = -3. Then find det(-A2B). -6 -12 6 12 [5 2 -2 3 -47 0 4 21 _0 Find the determinant of the matrix, A= 10 0 -2 3...
3. Let det(A) = 3 and det B = –2. Find the indicated determinants: (a) det(AB) (b) det(B-1A) (c) det(AAT) (d) det(3BT)
1. (10 points) Let A and B be 3 x 3 matrices, with det A = -3 and det B = 2. Compute (a) det AB (6) det B4 (c) det 3B (d) det A"B" AT (e) det B-AB
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...
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).
Question 1. La 1 2] Let A = 6 3 4 Lc 5 6 for some a, b, c ER such that det A = 12. (a) (9 points) Determine the dimension of the column space of A. (Th mine the rank of A.) Justify your answer. (h) (8 points) Calculate the determinant of La-1 1 2] 6 - 2 3 4 - 3 5 6 (c) (8 points) Calculate the determinant of La 3 37 6 7 6 |...
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...