Q7 (6 points) For what values of s is the matrix 1-1 2s s 12s invertible? + Drag

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Q7 (6 points) For what values of s is the matrix 1-1 2s s 12s invertible? + Drag and drop your images or click to browse Q8 (10 points) Recall that for any two matrices x n matrices A and B, we have det(AB) det[ A) det(B) (a) Suppose that A, B, C are n × n matrices such that det(A B) -8, det(AC) : 5, and det (A BC)-10. Find det(A). (b) Suppose that an n × n matrix A satisfies As A What are the possible values of the determinant of A? (c) Suppose that P is an invertible n × n matrix, and A-P i BP. Show that det (A) det (B).

Explanation / Answer

finding determinant of the matrix

(1 - s) ( s)(2s) - s*1 - 1 (4s + 8s ) + 2s ( 2 + s^2 )

2s^2 - 2s^3 - s - 12s + 4s + 2s^3 = 0

2s^2 + 3s - 12s = 0

s = 9/2 , s = 0

so matrix is invertible for

s = 0 , 9/2

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