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Question
`If [[x,3x- y],[2x+z,3y -w ]]=[[3,2],[4,7]]` find x,y,z,w
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Solution
Since all the corresponding elements of a matrix are equal,
`[[x 3x- y ],[2x+z 3y -w ]]=[[3 2],[4 7]]`
x=3 ...(1)
3x−y=2 ...(2)
Putting the value of x in eq. (2), we get
3(3)−y=2
⇒9−y=2
⇒−y=−7
⇒ y=7
2x+z=4 ...(3)
Putting the value of x in eq. (3), we get
2(3)+z=4
⇒6+z=4
⇒z=4−6
⇒z=−2
3y−w=7 ...(4)
Putting the value of y in eq. (4), we get
3(7)−w=7
⇒21−w=7
⇒21−7=w
⇒w=14
∴ x=3 , y=7, z=−2 and w=14
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