MATRIX MULTIPLICATION WORKSHEET ANSWERS

About "Matrix Multiplication Worksheet Answers"

Here we are going to see how to multiply two matrices. To understand the concept, let us look into some example problems.

Question 1 :

If A  =  

then compute A4

Solution : 

A4  =  A ⋅ A ⋅ A ⋅ A

  =  A⋅ A2

In order to find A4, let us multiply A2 and A2

Question 2 :

Consider the matrix

(i)  Show that Aα Aβ =  A(α+β)

(ii) Find all possible real values of α satisfying the condition Aα + AαT  =  I

Solution :

From the given question, if 

By multiplying Aα Aβ, we get

In the given question, by replacing α by (α + β), we get

Question 3 :

If A  =  

and such that (A− 2I)(A− 3I) = O, find the value of x.

Solution :

(A− 2I)(A− 3I) = O

By equating the corresponding terms, we get

2x - 2  = 0

x  =  2/2  =  1

Hence the value of x is 1.

Question 4 :

If A =

show that A2 is a unit matrix.

Solution :

Question 5 :

If A =

and A3 - 6A2 + 7A + KI  =  0, then find the value of k.

Solution :

21 - 30 + 7 + K  =  0

28 - 30 + k  =  0

-2 + k  =  0

k  =  2

The value of k is 2.

Question 6 :

Give your own examples of matrices satisfying the following conditions in each case:

(i) A and B such that AB  BA .

(ii) A and B such that AB = O = BA, A  O and B  O.

(iii) A and B such that AB = O and BA  O.

Question 7 :

Show that f (x) f ( y) = f (x + y), where f(x)  =  

Solution :

Let us find the product of f(x) and f(y)

  =  f(x + y)

Hence proved.

Question 8 :

If A is a square matrix such that A2 = A, find the value of 7A - (I + A)3.

Solution :

   =  7A - (I + A)3

  =  7A - (I3 + 3A2I + 3AI2 + A3)

  =  7A - (I + 3AI + 3AI + A2 ⋅ A)

The product of identity matrix and A is matrix A.

 =  7A - (I + 3A + 3A + A ⋅ A)

  =  7A - (I + 6A + A2)

  =  7A - (I + 6A + A)

  =  7A - (I + 7A)

  =  7A - I - 7A

  =  - I

After having gone through the stuff given above, we hope that the students would have understood "Matrix Multiplication Worksheet Answers". 

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