In this worksheet, we will practice using Cramer’s rule to solve a system of linear equations.
Q1:
Consider the following simultaneous equations: 3π₯+2π¦=8,β8π₯β9π¦=2.
Write the determinant Ξο.
Write the determinant Ξο.
Write the determinant Ξ.
Q2:
Consider the following linear system of equations in matrix form: ο9153ο οπ₯π¦ο=οβ1β3ο .
Q3:
Use determinants to solve the system β8π₯β4π¦=β8,9π₯β6π¦=β9.
Q4:
Use determinants to solve the system π₯β5π¦+3π§=5,3π₯β4π¦+2π§=β5,βπ₯+3π¦β2π§=β5.
Q5:
Use determinants to solve the system β9π₯=β8+8π¦,6π¦=7+3π₯.
Q6:
According to Cramerβs rule and given that Ξ=||3752||,Ξ=||β53β25||,οο write the simultaneous equations of the system.
Q7:
Use determinants to solve the system 5π₯=β2π¦β5+3π§,β3π₯βπ¦+1=2π§,2π¦βπ§=β5π₯+3.
Q8:
Is Cramerβs rule useful for finding solutions to systems of linear equations in which there is an infinite set of solutions?
Q9:
Noah is solving simultaneous equations using Cramerβs rule. He writes down the following: Ξ=ο1234β3β221β4ο€,Ξ=ο213β34β2β12β4ο€,Ξ=ο221β3β34β112ο€.οοο
What does he write down for Ξ?
Q10:
Solve, using Cramer's rule, the simultaneous equations |||β1π§β4π¦|||=23,|||2π¦β5π₯|||=13,||3π₯5π§||=51.
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