Let A and B be 3x3 matrices, with det A = 4 and det B =...

Question

Question

Let A and B be 3x3 matrices, with det A = 4 and det B = -2. Use properties of determinants to complete parts (a) through (e)

a. Compute det \(\mathrm{AB}\).

det \(\mathrm{AB}=\square\) (Type an integer or a fraction.)

b. Compute det \(5 \mathrm{~A}\).

det \(5 \mathrm{~A}=\square\) (Type an integer or a fraction.)

c. Compute det \(\mathrm{B}^{\top}\).

\(\operatorname{det} \mathrm{B}^{\top}=\square\) (Type an integer or a fraction.)

d. Compute \(\operatorname{det} A^{-1}\).

\(\operatorname{det} \mathrm{A}^{-1}=\square\) (Type an integer or a simplified fraction.)

e. Compute det \(\mathrm{A}^{3}\).

det \(\mathrm{A}^{3}=\square\) (Type an integer or a fraction.)

Answer 1

✔ Recommended Answer

Answer #2

source: Basic properties of determinants and their transposes

answered by: Tom Andy

Answer 2

Answer #1

Ans. Given 1A1=4 IBL = -2 ai TABI (AL IBI - = 4x-2 18 (bi 15A = (5) TAI 125 x 4 1500 ū IBTI Since 1 Bl= 1871 Hence IBT) = di

Answer 3

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