Lesson Worksheet: Three-by-Three Determinants Mathematics • 10th Grade

In this worksheet, we will practice evaluating 3 × 3 determinants using the cofactor expansion (the Laplace expansion) or the rule of Sarrus.

Q1:

Consider 𝐴=ο˜βˆ’65βˆ’326βˆ’899βˆ’7.

Write the determinant whose value is equal to the minor of the element π‘ŽοŠ¨οŠ©.

  • A||βˆ’6599||
  • B||6βˆ’89βˆ’7||
  • C||βˆ’6βˆ’32βˆ’8||
  • D||5βˆ’39βˆ’7||

Q2:

Find the value of ||||226βˆ’31βˆ’2βˆ’5βˆ’1βˆ’4||||.

Q3:

Evaluate||||1βˆ’9βˆ’6βˆ’8412βˆ’19||||.

Q4:

Find the value of ||||βˆ’6βˆ’27βˆ’694βˆ’201||||Γ—||βˆ’21βˆ’20||.

Q5:

Find the solution set of||||π‘₯00βˆ’1βˆ’5π‘₯021π‘₯||||=βˆ’80π‘₯.

  • A{4,βˆ’4}
  • B0,14,βˆ’14
  • C{0,4}
  • D14,βˆ’14
  • E{0,4,βˆ’4}

Q6:

Solve for π‘₯: ||||05βˆ’5π‘₯π‘₯45413||||=280.

  • Aπ‘₯=9 or π‘₯=4
  • Bπ‘₯=βˆ’9 or π‘₯=4
  • Cπ‘₯=βˆ’9 or π‘₯=βˆ’20
  • Dπ‘₯=9 or π‘₯=20

Q7:

Find the solution set of ||||βˆ’8π‘₯7π‘₯3π‘₯βˆ’2π‘₯0βˆ’5π‘₯βˆ’8π‘₯9π‘₯3π‘₯||||=736 in ℝ.

  • A{2}
  • B{βˆ’1}
  • C{βˆ’3}
  • D{βˆ’2}

Q8:

Determine the value of π‘˜ that makes π‘₯=4 a root of the equation ||||9π‘₯βˆ’3βˆ’4π‘₯+8βˆ’2π‘˜9π‘₯βˆ’3π‘₯βˆ’7βˆ’5||||=0.

  • Aβˆ’15
  • B32
  • C5
  • Dβˆ’12

Q9:

Consider the determinant ||||π‘₯𝑧𝑦𝑦π‘₯𝑧𝑧𝑦π‘₯||||. Given that π‘₯+𝑦+𝑧=βˆ’73 and π‘₯𝑦𝑧=βˆ’8, determine the determinant’s numerical value.

Q10:

Which of the following is equal to the determinant ||||π‘βˆ’8π‘π‘βˆ’7π‘Žπ‘Žβˆ’7𝑏8𝑐7π‘Ž7π‘βˆ’6βˆ’6βˆ’6||||?

  • A6(π‘Žβˆ’π‘)(7π‘βˆ’8𝑐)+42(π‘Žβˆ’π‘)
  • B6(π‘Žβˆ’π‘)(7π‘βˆ’8𝑐)βˆ’7(π‘Žβˆ’π‘)
  • C6(π‘Žβˆ’π‘)(7π‘βˆ’8𝑐)βˆ’42(π‘Žβˆ’π‘)
  • Dβˆ’42(π‘Žβˆ’π‘)βˆ’6(π‘Žβˆ’π‘)(7π‘βˆ’8𝑐)

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