OPERATIONS ON MATRICES WORKSHEET

Question 1 :

Add the following matrices.

Solution

Question 2 :

Find the sum of the following matrices

Solution

Question 3 :

Subtract the following matrices.

Solution

Question 4 :

Suppose the sum A+B+C exists. We also know that  has 2 rows and C has 3 columns. What can we say about matrix B ?

Solution

Question 5 :

Given that

Where O is the 2x2 zero matrix, find the value of x.

Solution

Question 6 :

Given that

find the values of x, y, z, a and b.

Solution

Question 7 :

then, verify that A + (B + C) = (A + B) + C

Solution

Question 8 :

then verify:

(i) A + B = B + A

(ii) A + (- A) = O = (- A) + A

Solution

Question 9 :

then find the additive inverse of A.

Solution

Question 10 :

If

then find AB and BA. Are they equal ?

Solution

Question 11 :

If

verify (AB)C  =  A(BC).

Solution

Question 12 :

If

verify that (AB)^T  =  B^TA^T 

Solution

Question 13 :

Prove that

are inverse to each other under matrix multiplication.

Solution

Question 14 :

If 

find (A + B)C and AC + BC. Is (A + B)C  =  AC + BC ?

Solution

Question 15 :

If A and B are square matrices such that

AB = I and BA = I 

then B is 

(A) Unit matrix

(B) Null matrix

(C) Multiplicative inverse matrix of A

(D) -A

Solution

Question 16 :

Find the values of x, y and z from the matrix equation

Solution

Question 17 :

Let 

Find the matrix C if C = 2A + B

Solution

Question 18 :

Solution

Question 19 :

Verify the property A(B + C) = AB + AC, when the matrices A, B, and C are given by

Solution

Question 20 :

Find the matrix A which satisfies the matrix relation 

Solution

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