Question

A is a square matrix of order 3 having a row of zeros, then the determinant of A is *

1

0

3

-2​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

A is a square matrix of order 3 having a row of zeros, then the determinant of A is 

(a) 1

(b) 0

(c) 3

(d) -2

EVALUATION

Here it is given that A is a square matrix of order 3

Then A has 3 rows and 3 columns

Now it is given that all three elements in the row is 0

So the determinant value of A is 0 if we expand it with respect to the Zero row

Hence the determinant of A is 0

For example let us take a matrix A with a zero row as below

$\sf{ A\: = }\displaystyle\begin{pmatrix} 0 & 0 & 0\\ x & y & z \\ c & d & e \end{pmatrix}$

Then

$\sf{ |A| \: = }\displaystyle\begin{vmatrix} 0 & 0 & 0\\ x & y & z \\ c & d & e \end{vmatrix}$

$\implies \sf{detA} = 0 + 0 + 0 \: (on \: expansion)$

$\implies \sf{detA} = 0$

FINAL ANSWER

Hence the correct option is :

A is a square matrix of order 3 having a row of zeros, then the determinant of A is 

(b) 0

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Answer 2

Answer:

B) 0

Explanation:

This Is The Correct Answer!

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