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Maths-

General

Easy

Question

If A= $open square brackets table row 1 3 row 3 4 end table close square brackets$ and A^2T– kA – 5I₂= O, then the value of k is-

3
5
7
–7

The correct answer is: 5

We are given with matrix A and also the equation of k and asked to find the value of k
$A squared minus 5 I subscript 2 space equals space end subscript open square brackets table row 1 3 row 3 4 end table close square brackets space open square brackets table row 1 3 row 3 4 end table close square brackets space minus 5 space open square brackets table row 1 0 row 0 1 end table close square brackets equals open square brackets table row 5 15 row 15 20 end table close square brackets space equals space 5 space open square brackets table row 1 3 row 3 4 end table close square brackets H e n c e space t h e space v a l u e space o f space k space equals 5$

Hence we find that the value of k is 5

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