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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

ConceptOperations on Matrices Properties of Scalar Multiplication of a Matrix

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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