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Find X And Y, If `X + Y = [(7,0),(2,5)] and X - Y = [(3,0),(0,3)] - CBSE (Science) Class 12 - Mathematics

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Question

Find X and Y, if `X + Y = [(7,0),(2,5)] and X - Y = [(3,0),(0,3)]`

Solution

`X + Y = [(7,0),(2,5)]` ....(1)

`X -Y = [(3,0),(0,3)]` ......(2)

Adding equations (1) and (2), we get:

`2X = [(7,0),(2,5)] + [(3,0),(0,3)] = [(7+3,0+0),(2+0, 5+3)] = [(10,0),(2,8)]`

`:. X = 1/2 [(10,0),(2,8)] = [(5,0),(1,4)]`

Now, `X + Y = [(7,0),(2,5)]`

`=> [(5,0),(1,4)] + Y = [(7,0),(2,5)]`

`=> Y = [(7,0),(2,5)] - [(5,0),(1,4)]`

`=> Y = [(7-5, 0-0),(2-1, 5-4)]`

`:. Y = [(2,0),(1,1)]`

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Solution Find X And Y, If `X + Y = [(7,0),(2,5)] and X - Y = [(3,0),(0,3)] Concept: Operations on Matrices - Properties of Scalar Multiplication of a Matrix.
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