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Maths-

General

Easy

Question

If A = $open square brackets table row 1 2 row 2 3 end table close square brackets$ and A² – KA– I₂ = 0, then value of K is-

4
2
1
– 4

hint Hint:

To multiply one matrix with another, we need to check first, if the number of columns of the first matrix is equal to the number of rows of the second matrix. Now multiply each element of the column of the first matrix with each element of rows of the second matrix and add them all.

The correct answer is: 4

$G i v e n space comma space A equals open square brackets table row cell 1 space space 2 end cell row cell 2 space space 3 end cell end table close square brackets space space space a n d space space space A squared minus K A minus I subscript 2 equals 0 W e space k n o w space t h a t space I subscript 2 equals space open square brackets table row cell 1 space space 0 end cell row cell 0 space space 1 end cell end table close square brackets a n d space A squared equals A. A space space space space equals space space space space open square brackets table row cell 1 space space 2 end cell row cell 2 space space 3 end cell end table close square brackets open square brackets table row cell 1 space space 2 end cell row cell 2 space space 3 end cell end table close square brackets space space space space space space space space space space space space space space U sin g space M u l t i p l i c a t i o n space o f space M a t r i c e s space space space space space space space space space space space space space space space space space equals open square brackets table row cell 1 plus 4 space space space space 2 plus 6 end cell row cell 2 plus 6 space space space space 4 plus 9 end cell end table close square brackets subscript 2 x 2 end subscript space space space space space space space space space space space space space space space space space space space space space space space equals open square brackets table row cell 5 space space 8 end cell row cell 8 space space 13 end cell end table close square brackets S u b s t i t u t i n g space t h e s e space v a l u e s space i n A squared minus K A minus I subscript 2 equals 0 open square brackets table row cell 5 space space 8 end cell row cell 8 space space 13 end cell end table close square brackets minus k open square brackets table row cell 1 space space 2 end cell row cell 2 space space 3 end cell end table close square brackets minus open square brackets table row cell 1 space space 0 end cell row cell 0 space space 1 end cell end table close square brackets equals space 0 open square brackets table row cell 5 space space space 8 end cell row cell 8 space space space 13 end cell end table close square brackets minus open square brackets table row cell 1 space space 0 end cell row cell 0 space space 1 end cell end table close square brackets equals k open square brackets table row cell 1 space space 2 end cell row cell 2 space space 3 end cell end table close square brackets open square brackets table row cell 4 space space 8 end cell row cell 8 space space 12 end cell end table close square brackets equals space k open square brackets table row cell 1 space space 2 end cell row cell 2 space space 3 end cell end table close square brackets T a k i n g space o u t space 4 space c o m m m o n space f r o m space L H S comma space w e space g e t 4 open square brackets table row cell 1 space space 2 end cell row cell 2 space space 3 end cell end table close square brackets equals space k open square brackets table row cell 1 space space 2 end cell row cell 2 space space 3 end cell end table close square brackets T h u s comma space k equals 4$

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