Skip to main contentSkip to solution

If [2x+15x0y2+1]=[x+310026]\begin{bmatrix}2x+1 & 5x \\ 0 & y^2+1\end{bmatrix} = \begin{bmatrix}x+3 & 10 \\ 0 & 26\end{bmatrix} then the possible values of x + y are:

Solution

✅ Correct Option: 3

When two matrices are equal, every element in the same position must be equal.

[2x+15x0y2+1]=[x+310026]\begin{bmatrix}2x+1 & 5x \\ 0 & y^2+1\end{bmatrix} = \begin{bmatrix}x+3 & 10 \\ 0 & 26\end{bmatrix}

Matching each position gives the following equations:

Top-left: 2x+1=x+32x+1 = x+3

Top-right: 5x=105x = 10

Bottom-left: 0=00 = 0 (always true)

Bottom-right: y2+1=26y^2+1 = 26


From the top-right equation:

5x=105x = 10

x=105x = \frac{10}{5}

x=2x = 2


From the bottom-right equation:

y2+1=26y^2 + 1 = 26

y2=25y^2 = 25

y=±5y = \pm 5

So y=5y = 5 or y=−5y = -5


Since x=2x = 2 and yy can be 55 or −5-5:

When y=5y = 5:

x+y=2+5=7x + y = 2 + 5 = 7

When y=−5y = -5:

x+y=2+(−5)=−3x + y = 2 + (-5) = -3

Therefore, the possible values of x+yx + y are 77 and −3-3.

Keyboard Shortcuts

  • Left arrow: Previous question
  • Right arrow: Next question
  • S key: Jump to solution
  • Q key: Jump to question