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In this lesson, we will learn how to multiply matrices.

Q1:

Given that π΄ is a matrix of order 2 Γ 3 and π΅ π is a matrix of order 1 Γ 3 , find the order of the matrix π΄ π΅ , if possible.

Q2:

Given that π΄ is a matrix of order 3 Γ 3 and π΅ π is a matrix of order 2 Γ 1 , find the order of the matrix π΄ π΅ , if possible.

Q3:

Given that π΄ is a matrix of order 1 Γ 2 and π΅ is a matrix of order 2 Γ 3 , find the order of the matrix π΄ π΅ , if possible.

Q4:

Is it possible to have a 2 Γ 1 matrix and a 1 Γ 2 matrix such that π΄ π΅ = οΌ 1 0 0 1 ο ? If so, give an example.

Q5:

Suppose the matrix product π΄ π΅ πΆ makes sense. We also know that π΄ has 2 rows, πΆ has 3 columns, and π΅ has 4 entries. Is it possible to determine the possible sizes of these matrices? If so, what are the possible sizes of π΄ , π΅ , and πΆ ?

Q6:

Find the matrices and such that, for any matrix , and . Explain why and are not the same.

Q7:

Suppose Which of the following products is defined?

Q8:

Suppose π΄ is a 1 Γ 2 matrix, π΅ is a 2 Γ 3 matrix, and πΆ is a 3 Γ 4 matrix. What are the sizes of the product matrices π΄ π΅ , π΅ πΆ , ( π΄ π΅ ) πΆ , and π΄ ( π΅ πΆ ) ?

Q9:

If π΄ is a matrix of order 1 Γ 1 and π΄ π΅ is a matrix of order 1 Γ 1 , then what is the order of π΅ ?

Q10:

If π΄ is a matrix of order 1 Γ 3 and π΄ π΅ is a matrix of order 1 Γ 3 , then what is the order of π΅ ?

Q11:

If π΄ is a matrix of order 3 Γ 2 and π΄ π΅ is a matrix of order 3 Γ 3 , then what is the order of π΅ ?

Q12:

Find a matrix such that for all matrices .

Q13:

Given that π΄ is a matrix of order π Γ π , and π΅ is a matrix of order π Γ π , determine the condition under which AB is defined.

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