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Find the matrices X and Y , if 2XY=[660421] and X+2Y=[325217]

Answer
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Hint: This problem can be treated as a linear equation in two variables in form of X and Y and solved just like how we solve a linear equation


Complete step-by-step answer:
The given matrices are
2XY=[660421](1)
X+2Y=[325217](2)
For performing the addition or subtraction of two matrices, the order of the matrices should be the same . The order of both the matrices is 2×3 .
Let’s suppose the matrices be X=[pqrstu] and Y=[abcdef]
After analyzing the two equations, it is clear that matrix Y can be eliminated for the calculation of matrix X by multiplying equation (1) by 2 and adding equation (1) and (2).
Multiplying equation (1) by (2),
2(2XY)=2[660421]
If a matrix is multiplied by a scalar quantity, then the scalar is to be multiplied by each and every term of the matrix as shown below,
4X2Y=[12120842](3)
Adding equation (2 ) and (3)
(X+2Y)+(4X2Y)=[325217]+[12120842]
For adding the two matrices , add their corresponding terms.
5X=[3+1221250281+47+2]5X=[151051055](4)
Now it is clear that in equation (4), we can take out 5 as a common factor.
5X=5[321211](5)
Cancelling 5 from both sides of LHS and RHS in equation (5), matrix X is obtained as
X=[321211](6)
Substitute the value of matrix X in equation (1),
2[321211]Y=[660421](7)
Multiply all the terms of the matrix X by 2 as given in the equation (7)
[642422]Y=[660421]
Now rearrange the terms and calculate the value of matrix Y as,
Y=[642422][660421]
Now subtract the 2 matrices by subtracting their corresponding terms,
Y=[022003]
Hence, the value of matrix X=[321211] and Y=[022003]..


Note: The important concepts to be remembered are
1)Two matrices can be added or subtracted only when they have the same order.
2)Multiplication of a matrix by a scalar, leads to multiplication of its terms.

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