If A= 5 & x y & 6 B= -4 & y -4 & 5 and A+B=1 then… - Vidyadip

Question

If $\text{A}=\displaystyle \begin{vmatrix} 5 &\text{amp; x} \\ \text{y} &\text{amp; 6} \end{vmatrix}\text{B}=\displaystyle \begin{vmatrix} -4 &\text{amp; y} \\-4 &\text{amp; 5} \end{vmatrix}$ and $\text{A}+\text{B}=1$ then the values of x and y respectively are:

-4, 4
-4, -4
4, 4
4, -4

✓

Answer

-4, 4

Solution:

$\text{A+B =1},\text{ i.e.,} \displaystyle \begin{vmatrix} 1&\text{amp; }\text{x+y} \\\text{y}-4 &\text{amp;} 1 \end{vmatrix}=\begin{vmatrix} 1&\text{amp; } 0 \\ 0 &\text{amp; } 1 \end{vmatrix}$

or $\text{x}=\text{y}=0,\text{ y}-4=0$

$\therefore\text{ x} = -4, \text{ y}=4$

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