The inverse of the matrix A =[ 2&0 &0 0&3& 0 0&0&4 ] is

Question

The inverse of the matrix A =[ 2&0 &0 0&3& 0 0&0&4 ] is (A) [ 2&0 &0 0&3& 0 0&0&4 ] (B) [ (1/2)&0 &0 0& (1/3)& 0 0&0& (1/4) ] (C)  (1/24)[ 2&0 &0 0&3& 0 0&0&4 ] (D) (1/24)[ beginarraylll1 0 0 0 1 0 0 0 1 endarray]

Tardigrade Admin · Accepted Answer

The inverse of a diagonal matrix is obtained by replacing each element in the diagonal with its reciprocal. Hence the answer here would be: A -1=[ beginarrayccc (1/2) 0 0 0 (1/3) 0 0 0 (1/4) endarray]

Q. The inverse of the matrix $A = ⎣ ⎡ 200030004 ⎦ ⎤$ is

$⎣ ⎡ 200030004 ⎦ ⎤$

$⎣ ⎡ \frac{1}{2} 00 0 \frac{1}{3} 0 00 \frac{1}{4} ⎦ ⎤$

$\frac{1}{24} ⎣ ⎡ 200030004 ⎦ ⎤$

$\frac{1}{24} ⎣ ⎡ 100010001 ⎦ ⎤$

The inverse of a diagonal matrix is obtained by replacing each element in the diagonal with its reciprocal. Hence the answer here would be:
$A^{- 1} = ⎣ ⎡ \frac{1}{2} 00 0 \frac{1}{3} 0 00 \frac{1}{4} ⎦ ⎤$

Q. The inverse of the matrix A=⎣⎡​200​030​004​⎦⎤​ is

⎣⎡​200​030​004​⎦⎤​

⎣⎡​21​00​031​0​0041​​⎦⎤​

241​⎣⎡​200​030​004​⎦⎤​

241​⎣⎡​100​010​001​⎦⎤​