Assertion (A) : If [ cc x y & 4 z+5 & x+y ]= [ cc 4 & w 0 & 4 ], … - Vidyadip

MCQ

Assertion (A) : If $\left[\begin{array}{cc}x y & 4 \\ z+5 & x+y\end{array}\right]=\left[\begin{array}{cc}4 & w \\ 0 & 4\end{array}\right]$, then $x=2, y=2, z=-5$ and $w=4$.
Reason (R) : Two matrices are equal, if their orders are same and their corresponding elements are equal.

✓
Both (A) and (R) are true and (R) is the correct explanation of (A).
B
Both (A) and (R) are true but (R) is not the correct explanation of (A).
C
(A) is true but (R) is false.
D
(A) is false but (R) is true.

✓

Answer

Correct option: A.

Both (A) and (R) are true and (R) is the correct explanation of (A).

(a) : $\left[\begin{array}{cc}x y & 4 \\ z+5 & x+y\end{array}\right]=\left[\begin{array}{cc}4 & w \\ 0 & 4\end{array}\right]$
On equating the corresponding elements, we get
$
x y=4, w=4, z+5=0 \text { and } x+y=4
$
On solving these equations, we get $x=2, y=2, z=-5$ and $w=4$. Also, the two matrices are equal, if their orders are same and their corresponding elements are equal.

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