Evaluate x^2&x^3&x^4 &y&z ^2&x^3&x^4 is: - Vidyadip

MCQ

Evaluate $\begin{bmatrix}\text{x}^2&\text{x}^3&\text{x}^4\\\text{x}&\text{y}&\text{z}\\\text{x}^2&\text{x}^3&\text{x}^4\end{bmatrix}$ is:

✓
$0$
B
$1$
C
$xyz$
D
$x^2 yz^3$

✓

Answer

Correct option: A.

$0$

$\begin{bmatrix}\text{x}^2&\text{x}^3&\text{x}^4\\\text{x}&\text{y}&\text{z}\\\text{x}^2&\text{x}^3&\text{x}^4\end{bmatrix}$
If the elements of any two rows or columns are identical, then the value of determinant is zero.
Here, the elements of row $1$ and row $3$ are identical.
Hence, its determinant is $0.$

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