
Find the matrices and , if and
Answer
493.8k+ views
Hint: This problem can be treated as a linear equation in two variables in form of and and solved just like how we solve a linear equation
Complete step-by-step answer:
The given matrices are
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 .
Let’s suppose the matrices be and
After analyzing the two equations, it is clear that matrix can be eliminated for the calculation of matrix by multiplying equation (1) by 2 and adding equation (1) and (2).
Multiplying equation (1) by (2),
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,
Adding equation (2 ) and (3)
For adding the two matrices , add their corresponding terms.
Now it is clear that in equation (4), we can take out 5 as a common factor.
Cancelling 5 from both sides of LHS and RHS in equation (5), matrix is obtained as
Substitute the value of matrix in equation (1),
Multiply all the terms of the matrix by 2 as given in the equation (7)
Now rearrange the terms and calculate the value of matrix as,
Now subtract the 2 matrices by subtracting their corresponding terms,
Hence, the value of matrix and ..
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.
Complete step-by-step answer:
The given matrices are
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
Let’s suppose the matrices be
After analyzing the two equations, it is clear that matrix
Multiplying equation (1) by (2),
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,
Adding equation (2 ) and (3)
For adding the two matrices , add their corresponding terms.
Now it is clear that in equation (4), we can take out 5 as a common factor.
Cancelling 5 from both sides of LHS and RHS in equation (5), matrix
Substitute the value of matrix
Multiply all the terms of the matrix
Now rearrange the terms and calculate the value of matrix
Now subtract the 2 matrices by subtracting their corresponding terms,
Hence, the value of matrix
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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