Let X=[ beginmatrix x y z endmatrix ],D=[ beginmatrix 3 5 11 endmatrix ] and A=[ beginmatrix 1 -1 -2 2 1 1 4 -1 -2 endmatrix ], if X=A-1D, then X is equal to:

Question

Let X=[ beginmatrix x y z endmatrix ],D=[ beginmatrix 3 5 11 endmatrix ] and A=[ beginmatrix 1 -1 -2 2 1 1 4 -1 -2 endmatrix ], if X=A-1D, then X is equal to: (A)  [ beginmatrix 1 0 2 endmatrix ]  (B)  [ beginmatrix (8/3) (-1/3) 0 endmatrix ]  (C)  [ beginmatrix (-8/3) 1 0 endmatrix ]  (D)  [ beginmatrix (8/3) (1/3) -1 endmatrix ]

Tardigrade Admin · Accepted Answer

∵ A=[ beginmatrix 1 -1 -2 2 1 1 4 -1 -2 endmatrix ] ∴ A-1=(1/3)[ beginmatrix -1 0 1 8 6 -5 -6 -3 3 endmatrix ] Now, A-1D=(1/3)[ beginmatrix -1 0 1 8 6 -5 -6 -3 3 endmatrix ][ beginmatrix 3 5 11 endmatrix ] =(1/3)[ beginmatrix 8 -1 0 endmatrix ] ⇒ [ beginmatrix x y z endmatrix ]=[ beginmatrix 8/3 -1/3 0 endmatrix ]

Q. Let $X = ⎣ ⎡ x y z ⎦ ⎤, D = ⎣ ⎡ 3511 ⎦ ⎤$ and $A = ⎣ ⎡ 124 - 1 1 - 1 - 2 1 - 2 ⎦ ⎤,$ if $X = A^{- 1} D,$ then $X$ is equal to:

$⎣ ⎡ 102 ⎦ ⎤$

$⎣ ⎡ \frac{8}{3} \frac{- 1}{3} 0 ⎦ ⎤$

$⎣ ⎡ \frac{- 8}{3} 10 ⎦ ⎤$

$⎣ ⎡ \frac{8}{3} \frac{1}{3} - 1 ⎦ ⎤$

$⎣ ⎡ \frac{8}{3} \frac{1}{3} 0 ⎦ ⎤$

Q. Let X=⎣⎡​xyz​⎦⎤​,D=⎣⎡​3511​⎦⎤​ and A=⎣⎡​124​−11−1​−21−2​⎦⎤​, if X=A−1D, then X is equal to:

⎣⎡​102​⎦⎤​

⎣⎡​38​3−1​0​⎦⎤​

⎣⎡​3−8​10​⎦⎤​

⎣⎡​38​31​−1​⎦⎤​