pls help Let A be a 4 times 4 matrix and B be obtained from A by adding 5 times

Question

pls help

Let A be a 4 times 4 matrix and B be obtained from A by adding 5 times the first row to each of the second and third rows, then det (B) = 5^4 det (A) True False (h) A square matrix D is invertible if and only if 1/det(D) exists as a real number True False (i) If a square matrix B is invertible, then its inverse has zero determinant. True False (j) In order to apply Cramer's Rule, the coefficient matrix of a system must be invertible and the determinant of the inverse of the coefficient matrix must be different from 0. True False

Explanation / Answer

1) false.....because det(A) and det(b) will be remain same...that is det(A)=det(B)...

2) true.....D is invertible if and only if det(D) is not equal to zero.

3) false....beacuse det(B1)= (det B)1

4) true....the determinant of the system must be non-zero and also matrix is invertible

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