Question

Find the values of the variables.

6
[+]
H
3
3
a.
-2
X = 7
y = 5
b. x = 12
y = -2
4 1
C.
X = 4
y = -2
d. x = 5
y = 1

Answer 1

x = 5, y = 1

Explanation:

If two matrices A and B of the same size m x n are added together to get the resultant matrix C then the elements of matrix C are obtained by

`c_(11) = a_(11) + b_(11)\\c_(12) = a_(12) + b_(12)\\...\\c_(mn) = a_(mn) + b_(mn)\\\\\rm{Here\:we\:have\:{a_(11)\:=\:x,\:b_(11)\:=\:y\:and\:c_(11)\:=\:6\:\par \par\\So we get x + y = 6 \cdots (1)\par\\`

Similarly

`a_(21) + b_(22) = c_(22)\\\\a_(21) = x, b_(22)= -y, c_(22) = 4\\\\ x - y = 4 \cdots(2)\\\\`

Add equations (1) and (2) to get

`x + y + x - y = 6 + 4`

`== > x + x = 10\\== > 2x = 10\\== > x = 5\\\\\textrm{Plug into equation (1)}\\\\x + y = 6 \\== > 5 + y = 6\\== > y = 6 - 5 = 1\\\\\rm{Solution \par \parx = 5, y = 1\\`