If A=1 33 4 and A2−kA−5I2=O, then the value of k is

Solution:

We have,

$A^{2} - 5 I_{2} = [\begin{array}{ll} 10 15 \\ 15 25 \end{array}] - [\begin{array}{ll} 5 0 \\ 0 5 \end{array}] = [\begin{array}{rr} 5 15 \\ 15 20 \end{array}] = 5 A .$

$∴ k = 5$

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