The inverse of the matrix X=\left[\begin{array}{ccc}2 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & 4]\end{array} is

Correct Answer is : [1∕20001∕30001∕4]

24\left[\begin{array}{ccc}1 \/ 2 & 0 & 0 \ 0 & 1 \/ 3 & 0 \ 0 & 0 & 1 \/ 4]\end{array}

\frac{1}{24}\left[\begin{array}{ccc}1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1]\end{array}

\frac{1}{24}\left[\begin{array}{ccc}2 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & 4]\end{array}

\left[\begin{array}{ccc}1 \/ 2 & 0 & 0 \ 0 & 1 \/ 3 & 0 \ 0 & 0 & 1 \/ 4]\end{array}

CBSE Class 12 Math 2022 Term I Solved Paper - Question 44

Question : 44 of 50

Marks: +1, -0

The inverse of the matrix

X={[\table 2 , 0 , 0 ; 0 , 3 , 0 ; 0 , 0 , 4]}

Solution:

The inverse of a diagonal matrix is obtained by replacing each element in the diagonal with its reciprocal.
Since,

X={[\table 2 , 0 , 0 ; 0 , 3 , 0 ; 0 , 0 , 4 ]}

Therefore

X^{-1}={[\table \;{1}/{2} , 0 , 0 ; 0 , \;{1}/{3} , 0 ; 0 , 0 , \;{1}/{4} ]}

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