Matrix Operations Practice :
Here we are going to see some practice questions on matrix operations.
Question 1 :
Verify the property A(B + C) = AB + AC, when the matrices A, B, and C are given by
Solution :
In order to verify the given statement A(B + C) = AB + AC, first we have to calculate the terms which is inside the parenthesis.
Now we have to find the product of the matrices A and (B + C)
Hence the value of A(B + C) is the matrix given above.
Now let us do calculation in right hand side.
In order to find the value of AB, we have to multiply the matrices A and B.
In order to find the value of AC, we have to multiply the matrices A and C.
Now we have to add the above matrices AB and AC.
Since we got the same answer for A(B + C) and AB + AC, we may decide that L.H.S = R.H.S
Hence it is proved.
Question 2 :
Find the matrix A which satisfies the matrix relation
Solution :
By multiplying the matrix A with order m x n by the given matrix with order 2 x 3, we get a matrix with order 2 x 3.
So the required matrix will be in the order 2 x 2.
Let us equate the corresponding terms.
a + 4b = -7 -------(1)
2a + 5b = -8 -------(2)
c + 4d = 2 -------(3)
2c + 5d = 4 -------(4)
By solving the first and second equations, we get the values of a and b respectively.
(1) - (2)
(2a + 8b) - (2a + 5b) = -14 - (-8)
2a + 8b - 2a - 5b = -14 + 8
3b = -6
b = -6/3 ==> -2
Applying the value of b in first equation, we get
a + 4(-2) = -7
a - 8 = -7
a = -7 + 8 ==> 1
By solving the third and fourth equations, we get the values of a and b respectively.
2(3) - (4)
2c + 8d - (2c + 5d) = 4 - 4
2c + 8d - 2c - 5d = 0
3d = 0 ==> d = 0
Applying the value of b in third equation, we get
c + 4(0) = 2
c = 2
After having gone through the stuff given above, we hope that the students would have understood "Matrix Operations Practice".
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