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In this lesson, we will learn how to use operations on matrices, such as addition, subtraction, and scalar multiplication, to find the values of unknown variables.

Q1:

If π΄ = π΅ π , where what are the values of π and π ?

Q2:

Given that find the values of π₯ , π¦ , π§ , and π .

Q3:

Given that find the values of π₯ , π¦ , and π§ .

Q4:

Q5:

Let π΄ = ( β 2 3 ) , and π΅ = ( 1 2 ) . Find π and π‘ satisfying π + π‘ = 1 such that π π΄ + π‘ π΅ = ( π π ) for some number π . Also give the number π .

Q6:

Given that find π₯ , π¦ , and π§ .

Q7:

Determine the values of π₯ , π¦ , π , and π that satisfy the given equation where π is the zero matrix of order 2 Γ 2 .

Q8:

Given that what are the values of π₯ , π¦ , and π§ ?

Q9:

Write the matrix οΌ 3 β 8 β 1 β 9 ο in the form π οΌ 1 0 0 0 ο + π οΌ 0 1 0 0 ο + π οΌ 0 0 1 0 ο + π οΌ 0 0 0 1 ο , where π , π , π , and π are real numbers that you should find.

Q10:

Let π΄ = οΌ 1 2 3 4 ο and π΅ = οΌ 1 2 1 π ο . Is it possible to choose a value for π so that π΄ π΅ = π΅ π΄ ? If so, what is this value?

Q11:

Consider the shown matrices Is it possible to choose π such that π΄ π΅ = π΅ π΄ ? If so, what should π be equal to?

Q12:

Consider the matrices If π΄ π΅ = π΅ π΄ , what are the values of π₯ and π¦ ?

Q13:

Given that where πΌ is the unit matrix, determine the value of π₯ .

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