If A, B and C are square matrices of order 3 such that A = [ * 20… - Vidyadip

MCQ

If $A$, $B$ and $C$ are square matrices of order $3$ such that $A = \left[ {\begin{array}{*{20}{c}} x&0&1 \\ 0&y&0 \\ 0&0&z \end{array}} \right]$ and $\left| B \right| = 36$, $\left| C \right| = 4$, $\left( {x,y,z \in N} \right)$ and $\left| {ABC} \right| = 1152$ then the minimum value of $x + y + z$ is

✓
$6$
B
$8$
C
$10$
D
$12$

✓

Answer

Correct option: A.

$6$

a
$|A|=x y z$

$|A B C|=x y z \times 36 \times 4=1152$

$x y z=8$

$\frac{x+y+z}{3} \geq \sqrt[3]{8}$

$x+y+z \geq 6$

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