Q35. Give an example of two matrices ... [FREE SOLUTION]

Chapter 4: Q35. (page 172)

Give an example of two matrices A and B whose product is commutative so that $A B = B A$

Short Answer

Expert verified

The required matrices are $A = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$ and $B = [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}]$

Step by step solution

Step 1- Determine the dimensions of the required matrices

The dimensions for both the matrices should be same so the dimensions $2 脳 2$ are the best choice.

– Write the matrices

Each matrix should contain 0 in place of first row and second column along with the second row and first column so write the matrices.

$A = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$ $B = [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}]$

Step 3- Check the matrices

Perform multiplication between the obtained matrices A and B.

$\begin{matrix} A B = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] 鈰� [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}] \\ = [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}] \end{matrix}$

Now, perform multiplication between B and A.

$\begin{matrix} B A = [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}] 鈰� [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] \\ = [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}] \end{matrix}$

Step 3- Make the conclusion

As the obtained matrices are satisfying the commutative property $A B = B A$ so the obtained matrices are the required matrices.

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91影视

Give an example of two matrices A and B whose product is commutative so that $A B = B A$

Short Answer

Step by step solution

Step 1- Determine the dimensions of the required matrices

– Write the matrices

Step 3- Check the matrices

Step 3- Make the conclusion

One App. One Place for Learning.

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91影视

Give an example of two matrices A and B whose product is commutative so thatAB=BA

Short Answer

Step by step solution

Step 1- Determine the dimensions of the required matrices

– Write the matrices

Step 3- Check the matrices

Step 3- Make the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Decision Maths

Pure Maths

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Give an example of two matrices A and B whose product is commutative so that $A B = B A$