In this worksheet, we will practice evaluating 3 × 3 determinants using the cofactor expansion (the Laplace expansion) or the rule of Sarrus.
Q1:
Consider π΄=οβ65β326β899β7ο€.
Write the determinant whose value is equal to the minor of the element πο¨ο©.
Q2:
Find the value of ||||226β31β2β5β1β4||||.
Q3:
Evaluate||||1β9β6β8412β19||||.
Q4:
Find the value of ||||β6β27β694β201||||Γ||β21β20||.
Q5:
Find the solution set of||||π₯00β1β5π₯021π₯||||=β80π₯.
Q6:
Solve for π₯: ||||05β5π₯π₯45413||||=280.
Q7:
Find the solution set of ||||β8π₯7π₯3π₯β2π₯0β5π₯β8π₯9π₯3π₯||||=736 in β.
Q8:
Determine the value of π that makes π₯=4 a root of the equation ||||9π₯β3β4π₯+8β2π9π₯β3π₯β7β5||||=0.
Q9:
Consider the determinant ||||π₯π§π¦π¦π₯π§π§π¦π₯||||. Given that π₯+π¦+π§=β73ο©ο©ο© and π₯π¦π§=β8, determine the determinantβs numerical value.
Q10:
Which of the following is equal to the determinant ||||πβ8ππβ7ππβ7π8π7π7πβ6β6β6||||?
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