Question

If 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

Answer:

correct answer is zero (0).

Answer 2

Given :   A is a square matrix of order 3 having a row of zeros

To Find : determinant of A

1

0

3

-2​

Solution:

determinant of A = 0

| A |  = 0

$A=\left[\begin{array}{ccc}0&0&0\\a&b&c\\d&e&f\end{array}\right]$

| A |  = 0 (bf - ec)  - 0(af - cd)  + 0(ae - bd)

= 0 - 0 + 0

= 0

$A=\left[\begin{array}{ccc}a&b&c\\0&0&0\\d&e&f\end{array}\right]$

| A |  =a(0 - 0)  - b(0 - 0)  + c(0 - 0)

= 0 - 0 + 0

= 0

$A=\left[\begin{array}{ccc}a&b&c\\d&e&f\\0&0&0\end{array}\right]$

| A |  =a(0 - 0)  - b(0 - 0)  + c(0 - 0)

= 0 - 0 + 0

= 0

determinant of A is   0  if a  having a row of zeros

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