Question

What is 'a', if [(1,4) (2,a)] is a singular matrix​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{\left(\begin{array}{cc}1&4\\2&a\end{array}\right)\;is\;a\;singular\;matrix}$

$\underline{\textbf{To find:}}$

$\textsf{The value of 'a'}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Singular matrix:}}$

$\textsf{A square matrix A is said to be singular if}\;\mathsf{|A|=0}$

$\mathsf{Since\;\left(\begin{array}{cc}1&4\\2&a\end{array}\right)\;is\;a\;singular\;matrix,\;we\;have}$

$\mathsf{\left|\begin{array}{cc}1&4\\2&a\end{array}\right|=0}$

$\implies\mathsf{1{\times}a-2{\times}4=0}$

$\implies\mathsf{a-8=0}$

$\implies\boxed{\mathsf{a=8}}$

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Answer 2

SOLUTION

TO DETERMINE

The value of a such that the below matrix is singular

$\displaystyle\begin{pmatrix} 1 & 4\\ 2 & a \end{pmatrix}$

CONCEPT TO BE IMPLEMENTED

A Matrix M is said to be singular matrix if

det M = 0

EVALUATION

Here the given matrix is

$\displaystyle\begin{pmatrix} 1 & 4\\ 2 & a \end{pmatrix}$

Let A be the given matrix

Then

$A= \displaystyle\begin{pmatrix} 1 & 4\\ 2 & a \end{pmatrix}$

Now

$det \: A= \displaystyle\begin{vmatrix} 1 & 4\\ 2 & a \end{vmatrix}$

$\implies \sf{ det \: A= 2a - 8 }$

Since A is a singular matrix

So det A = 0

$\implies \sf{ 2a - 8 = 0}$

$\implies \sf{ 2a = 8}$

$\implies \sf{ a = 4}$

FINAL ANSWER

Hence the required value of a = 4

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