Compute the determinant of the matrix [[2,0,1], [-1,5,2], [3,4,0]].

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

Compute the determinant of the matrix [[2,0,1], [-1,5,2], [3,4,0]].

Explanation:
Determinants of 3×3 matrices can be found by expanding along a row using cofactors. Using the standard formula det = a(ei − fh) − b(di − fg) + c(dh − eg) for the matrix with rows a b c, d e f, g h i, assign a=2, b=0, c=1, d=-1, e=5, f=2, g=3, h=4, i=0. Compute ei − fh = 5·0 − 2·4 = -8; di − fg = (-1)·0 − 2·3 = -6; dh − eg = (-1)·4 − 5·3 = -19. Then det = 2·(-8) − 0·(-6) + 1·(-19) = -16 + 0 - 19 = -35. Thus the determinant is -35.

Determinants of 3×3 matrices can be found by expanding along a row using cofactors. Using the standard formula det = a(ei − fh) − b(di − fg) + c(dh − eg) for the matrix with rows a b c, d e f, g h i, assign a=2, b=0, c=1, d=-1, e=5, f=2, g=3, h=4, i=0. Compute ei − fh = 5·0 − 2·4 = -8; di − fg = (-1)·0 − 2·3 = -6; dh − eg = (-1)·4 − 5·3 = -19. Then det = 2·(-8) − 0·(-6) + 1·(-19) = -16 + 0 - 19 = -35. Thus the determinant is -35.

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