Question

linear algebra question... see attachment please

Answer 1

det( A*B) = det A*det B
det A^t = det A
det (kA_3) = k^3 det A
det A^-1 = 1/det A
Now apply

Answer 2

det (kA_3) = k^3 det A could you explain this part?

Answer 3

what is the underscore?

Answer 4

underscore is size of the matrix

Answer 5

your matrix is 3 x 3, hence the coefficient of solution should be k ^3 or 3^3 =9

Answer 6

If you multiply one row by a constant, the determinant is multiplied by that constant. If you multiply the whole matrix by a constant, then you multiply every row in that matrix by that constant. Therefore, the determinant is \(k^n\det(A)\) where k is the constant and n is the number of rows or columns of A.

Answer 7

I mean \(\det(kA)=k^n\det(A)\).