If A, B, and Care 2x2 matrices; and det(A) = -2, det(B) = -3, and det(C)=-4 then compute: det(4C^TA^-1 C^TB^3) = 0 Official Time

Question

omeli [17]

3 years ago

8

If A, B, and Care 2x2 matrices; and det(A) = -2, det(B) = -3, and det(C)=-4 then compute: det(4C^TA^-1 C^TB^3) = 0 Official Time

: 12:46:13 SUBMIT AND MARK SAVE AND CLOSE

Mathematics

1 answer:

almond37 [142] · Answer 1 · 2022-07-04T01:10:25+03:00

almond37 [142]3 years ago

3 0

Answer with explanation:

|A| = -2

|B|= -3

|C| = -4

$|4 C^TA^{-1}C^TB^{3}|=4 |C||A|^{-1}|C||B|^3, \text{as}|C^T|=|C|,|A^n|=A^n\\\\=4 \times (-4) \times (-2)^{-1} \times (-4) \times (-3)^3\\\\=4 \times (-4) \times \frac{-1}{2} \times (-4) \times (-27)\\\\=-1728 \times \frac{-1}{2} \\\\=864$