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Maths-

General

Easy

Question

If A = $open square brackets table row 3 1 row 7 5 end table close square brackets$ and A² + kI = 8A, then k equals

4
8
¼
1/16

The correct answer is: 8

To find the value of k.
Given, A = $open square brackets table row 3 1 row 7 5 end table close square brackets$ and $A squared$ + kI = 8A.
$open square brackets table row 3 1 row 7 5 end table close square brackets$ x $open square brackets table row 3 1 row 7 5 end table close square brackets$ + k x $open square brackets table row 1 0 row 0 1 end table close square brackets$ = 8 x $open square brackets table row 3 1 row 7 5 end table close square brackets$
$open square brackets table row 16 8 row 56 32 end table close square brackets$ + $open square brackets table row k 0 row 0 k end table close square brackets$ = $open square brackets table row 24 8 row 56 40 end table close square brackets$
comparing on both sides,
16+k=24
k=8

Therefore, the value of k is 8.

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