Maths-
General
Easy
Question
If A=
and A2T – 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](data:image/png;base64,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)
Hence we find that the value of k is 5
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