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Find all the values of k for which the following matrix is invertible [k-1 k-1 0...
Problem 12. (6 points) Determine all values of k for which the following matrix is invertible. [1 -1 21 1 1 k | 2 4 k²
ſi 0 0] 1. Determine for what values of k e R the matrix is invertible A = -1 1 k . 0 1 4k
4. (3 points) Find all values of x so that the following matrix is invertible: 2 2 0 1 2 3 0 2 -C 1 0 3 0 A= 0 0 0 0 2-3
Find all values of k that make the fol- Problem 7 lowing matrix singular: [i 20 k] 1 1 k k2 1 0 1 k 0 1 1 2
Question 7 [10 points) Find conditions on k that will make the matrix A invertible. To enter your answer first select 'always', never', or whether should be equal or not equal to specific values, then enter a value or a list of values separated by commas. k 0 2 A-8k-2 4 2-1 A is invertible: Always Always Never Question 8 [10 When k = Express the follow. When katrix A as a product of elementary matrices:
For the following problems use: Annx n matrix A is invertible RREF(A) = I rank(A) - n A 2 x 2 matrix A is invertible = det(A) 0 3 singular (non-invertible). For which value(s) of h is A = -2 -1 -4 Choose... Choose... 6 2 h-2 a 0,b 0,c+0,d +0 A = 4 -1 C 0 x-2 or x 4 For which values of x is A = invertible a 0,b 0,c 0,d=0 4 x 2 X#1 and x2...
Determine if each following matrix is invertible. If so, find the inverse matrix. [1 0 1 2 2 3] 12 -1 3 5 -1
9. Find the inverse of the matrix [1 1 k in terms of k Determine all value(s) of k for which the above matrix is not invertible.
с 1 0 3. Use determinants to find which real values of c make the matrix 0 2c invertible. -1 c1 4. Find the characteristic polynomial, the eigenvalues and corresponding eigenvectors of each of the following matrices. --2 1 2 (b) 2 6 -6 3 3 2 2
2 invertible? C For which values of c is the matrix 8 O c 4 c =-4 Both of the above, i.e., c +4 Neither of the above, i.e., c +4. Suppose that the following row operations: interchange rows 1 and 3 multiply row 3 by 1/2 add -3 times row 1 to row 2 2 1 7 in this order, transform a matrix A into B = | 0 4-5 L0 0 3 What is the determinant of A?...