Question -
Answer -
Given
Given that two matrices are equal.
We know that if two matrices are equal then the elements of eachmatrices are also equal.
Therefore by equating them we get,
3x + 4y = 2┬атАжтАж┬а(1)
x тАУ 2y = 4┬атАжтАж┬а(2)
a + b = 5┬атАжтАж (3)
2a тАУ b = тАУ 5┬атАжтАж (4)
Multiplying equation (2) by 2 and adding to equation (1), we get
3x + 4y + 2x тАУ 4y = 2 + 8
тЗТ┬а5x= 10
тЗТ┬аx= 2
Now, substituting the value of x in equation (1)
3 ├Ч 2 + 4y = 2
тЗТ┬а6+ 4y = 2
тЗТ┬а4y= 2 тАУ 6
тЗТ┬а4y= тАУ 4
тЗТ┬аy= тАУ 1
Now by adding equation (3) and (4)
a + b + 2a тАУ b = 5 + (тАУ 5)
тЗТ┬а3a= 5 тАУ 5 = 0
тЗТ┬аa= 0
Now, again by substituting the value of a in equation (3), weget
0 + b = 5
тЗТ┬аb= 5
тИ┤┬аa= 0, b = 5, x = 2 and y = тАУ 1