your answers. (a) Kvery mairix A has a detecminnt. (b) If A is an nxn matrix the

Question

your answers. (a) Kvery mairix A has a detecminnt. (b) If A is an nxn matrix then each cofactor of A is an (n-1)x (n-1) matrix (c) If A is an n x n matrix with all positive entries then det(A) > 0. (d) If A is an n × n matrix with cof(A)a -cof(A)i2 cof(A)in-0, for some i, then det(A) = 0. (e) If A is a diagonal matrix then adj(A) is a diagonal matrix. (f) If adja has no zero entry then det A 0. (g) If A and B are 2 x 2 matrices then det(A-B) = det(A)-det(B). (h) If A is a 3 x 3 matrix then adj(2A) = 2(adj). (i) If A is a square matrix then (adjA)T adj(AT) (j) If A and B are n x n matrices then det(AB) = det(BA)

Explanation / Answer

a. False. The determinant only exists for square matrices.

b. False. Each co-factor is created by removing one column and one row from A, but each co factor is a determinant.

c. False. If A =

1

3

2

1

then det(A) = 1-6 = -5 < 0.

d. True. The co-factor expansion can be done by starting with any row.

e. True as the co-factors of all non-diagonal entries will be 0.

Please post the remaining parts again. Meximum 4 at a time.

1

3

2

1

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