Determinants JEE2

Algebra Level 3

Let $A=\left| \begin{matrix} { x }^{ 2 } & 6 & 8 \\ 3 & y^{ 2 } & 9 \\ 4 & 5 & { z }^{ 2 } \end{matrix} \right| ,B=\left| \begin{matrix} 2x & 3 & 5 \\ 2 & 2y & 6 \\ 1 & 4 & 2z-3 \end{matrix} \right|$

If $\text{trace}(A)=\text{trace}(B)$ , then $x+y+z$ is equal to

The first part is here

6 None of these 0

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5 25

1 solution

Sujoy Roy
Mar 5, 2015

Here $A$ and $B$ are matrices, not determinants.

As $trace{A}=trace{B}$ ,

$x^2+y^2+z^2=2x+2y+2z-3$

or, $(x-1)^2+(y-1)^2+(z-1)^2=0$

or, $x=y=z=1$

or, $x+y+z=\boxed{3}$ .

Determinants JEE2

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