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In this lesson, we will learn how to use operation on matrices and matrix inversion to find an unknown matrix as an introduction to solve a system of linear equations.

Q1:

Consider the matrices Find the matrix π that satisfies the equation π = π΄ + π΅ π π π .

Q2:

Consider the matrices Find the matrix π that satisfies the equation π = π΄ β π΅ π π π .

Q3:

Q4:

Given that what are π and π ?

Q5:

Q6:

Find the matrix π΄ that satisfies the equation π΄ β 2 π΄ = οΌ 5 β 9 9 1 ο π .

Q7:

Given that find the matrix π΄ .

Q8:

Q9:

Given that solve the equation

Q10:

Determine π , given that

Q11:

Given that find the matrix π .

Q12:

Consider the matrices Determine the matrix π that satisfies β π = π΄ + ( π΅ πΆ ) π 2 π .

Q13:

Consider the matrices π΄ and π΅ : Find π΄ + π΅ β 1 2 .

Q14:

Given that determine the matrix π that satisfies the relation π = ( π΄ π΅ + π΄ πΆ ) π .

Q15:

Solve the matrix equation β 3 ο π + οΌ 3 6 5 7 ο ο = β π + οΌ β 5 4 1 7 ο .

Q16:

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

Q17:

Q18:

Given that π = ο 5 6 β 5 β 4 ο , find the values of π₯ and π¦ that satisfy π + π₯ π + π¦ πΌ = π ο¨ , where π is the zero matrix of order 2 Γ 2 and πΌ is the unit matrix of order 2 Γ 2 .

Q19:

Adam guesses that any matrix , where , must be a combination of and . In other words, it must be for some numbers and . Ramy wants to challenge this, since he see that produces the same product when multiplied on either side. Help Adam by finding and so that

Q20:

Given that

solve the following matrix equation for :

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