Question

if a=( 2 4 -1 k) a2=0. find the value of k. where 0 is null matrix​

Answer 1

Given :   $A=\left[\begin{array}{ccc}2&4\\-1&k\end{array}\right]$   , A² = 0

To Find :  Value of k

Solution:

$A=\left[\begin{array}{ccc}2&4\\-1&k\end{array}\right]$

A² = A x A

$A^2=\left[\begin{array}{ccc}2&4\\-1&k\end{array}\right] \times \left[\begin{array}{ccc}2&4\\-1&k\end{array}\right]$

$A^2=\left[\begin{array}{ccc}2\times 2 +4\times-1&2\times 4 +4\times k\\-1\times 2 +k\times-1&-1\times 4 +k\times k\end{array}\right]$

$A^2=\left[\begin{array}{ccc}0&8+4k\\-2-k&-4+k^2\end{array}\right]$

A² = 0

=> 8 + 4k = 0  => k = - 2

-2 - k = 0 => k  = - 2

-4 + k² = 0  => k = ± 2

Common from all  k = - 2

Value of k is - 2

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Answer 2

Given, [2 4

-1 k] and A2=0

Therefore, A2=[2 4]×[2 4]

-1 k -1 k

⇒[4−4−2−k8+4k−4+k2]=0

⇒[0−2−k8+4k−4+k2]=0

⇒8+4k=0

⇒8=−4k

⇒k=−2