(a) Show that if is a block diagonal matrix, where A and B are square matrices, then det D det A det B (b) Prove that the same holds for a block upper triangular matrix (c) Use this method to compute the determinant of the following matrices (i) (ii) (iii) (iv) 8 det(3 S) det A det B 257 243 5532 2012 2 00 1300 04 0 2130 1300 0025 0049 1542 5223

Question: (a) Show that if is a block diagonal matrix, where A and B are square matrices, then det D = det A det B. (b)

(a) Show that if

is a block diagonal matrix, where A and B are square matrices, then det D = det A det B.
(b) Prove that the same holds for a block upper triangular matrix

(ii)

(a) Show that if
is a block diagonal matrix, where A

(iii)

(iv)

8 det(3 S) = det A det B 257 243 5532 2012 2]00 1300 04-0 2130 1300 0025 0049 1542 5223

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