If D = \(\begin{bmatrix}2& -1&3\\4&1&2\\1&-3&1\\\end{bmatrix}\)
Find |D|
Find |D|
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Correct Answer: Option C
Explanation:
\(\begin{bmatrix}2& -1&3\\4&1&2\\1&-3&1\\\end{bmatrix}\)
= 2[(1 x 1) - (2 x -3)] - (-1)[(4 x 1) - (2 x 1)] + 3[(4 x -3) - (1 x 1)]
= 2(1 - (-6)) + 1(4 - 2) + 3(-12 - 1)
= 2(1 + 6) + 1(2) + 3(-13)
= 2(7) + 1(2) + 3(-13)
= 14 + 2 - 39
∴ |D| = -23
\(\begin{bmatrix}2& -1&3\\4&1&2\\1&-3&1\\\end{bmatrix}\)
= 2[(1 x 1) - (2 x -3)] - (-1)[(4 x 1) - (2 x 1)] + 3[(4 x -3) - (1 x 1)]
= 2(1 - (-6)) + 1(4 - 2) + 3(-12 - 1)
= 2(1 + 6) + 1(2) + 3(-13)
= 2(7) + 1(2) + 3(-13)
= 14 + 2 - 39
∴ |D| = -23