Worksheet: Two-by-Two Determinants

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In this worksheet, we will practice identifying determinants and evaluating 2x2 determinants.

Q1:

Find all the values of π‘₯ for which ||π‘₯βˆ’2βˆ’2π‘₯||+||6318||=45.

  • A2 or βˆ’2
  • B1 or βˆ’1
  • C1
  • D4 or βˆ’4
  • E4

Q2:

Solve ||π‘₯54βˆ’9||=16.

  • Aπ‘₯=36
  • Bπ‘₯=49
  • Cπ‘₯=βˆ’209
  • Dπ‘₯=βˆ’4

Q3:

Solve||π‘₯2βˆ’5π‘₯||βˆ’||βˆ’523π‘₯||=10.

  • A2 or 3
  • Bβˆ’2 or βˆ’3
  • C2 or 1
  • Dβˆ’5 or βˆ’2
  • Eβˆ’1 or 3

Q4:

Expand |||π‘Ž+π‘₯5π‘Žπ‘+7π‘¦βˆ’7𝑏|||.

  • Aβˆ’7𝑏π‘₯βˆ’35π‘Žπ‘¦
  • Bβˆ’7𝑏π‘₯+35π‘Žπ‘¦βˆ’2π‘Žπ‘
  • Cβˆ’7𝑏π‘₯βˆ’35π‘Žπ‘¦βˆ’12π‘Žπ‘
  • Dβˆ’7𝑏π‘₯βˆ’12π‘Žπ‘
  • Eβˆ’7𝑏π‘₯βˆ’35π‘Žπ‘¦βˆ’2π‘Žπ‘

Q5:

Find the value of the determinant |||πœƒπœƒβˆ’πœƒπœƒ|||cottancottan.

Q6:

Find the value of |||βˆ’3π‘₯+34π‘₯+4βˆ’3𝑦+4βˆ’π‘¦+3|||.

  • A15π‘₯π‘¦βˆ’9π‘₯βˆ’3π‘¦βˆ’16π‘₯+12π‘¦βˆ’7
  • B15π‘₯π‘¦βˆ’25π‘₯+9𝑦+12π‘₯π‘¦βˆ’7
  • C3π‘₯π‘¦βˆ’3π‘₯βˆ’π‘¦+12π‘₯π‘¦βˆ’4π‘₯+3π‘¦οŠ¨οŠ¨οŠ¨οŠ¨
  • D3π‘₯π‘¦βˆ’25π‘₯+9𝑦+12π‘₯π‘¦βˆ’7
  • E3π‘₯π‘¦βˆ’9π‘₯βˆ’3𝑦+12π‘₯π‘¦βˆ’16π‘₯+12π‘¦βˆ’7

Q7:

Evaluate |||βˆ’48πœƒβˆ’πœƒ2πœƒ|||.secsectan

Q8:

Find all the values of π‘₯ for which ||π‘₯βˆ’5βˆ’5π‘₯||+||1βˆ’248||=40.

  • A7 or βˆ’7
  • B8 or βˆ’8
  • C64
  • D49 or βˆ’49
  • E49

Q9:

Solve||π‘₯3βˆ’4π‘₯||+||62βˆ’4π‘₯||=12.

  • A4 or 2
  • Bβˆ’4 or βˆ’2
  • C4 or 1
  • Dβˆ’4 or βˆ’3
  • Eβˆ’1 or 2

Q10:

Solve ||π‘₯310βˆ’5||=βˆ’40.

  • Aπ‘₯=βˆ’70
  • Bπ‘₯=βˆ’10
  • Cπ‘₯=14
  • Dπ‘₯=βˆ’6
  • Eπ‘₯=2

Q11:

Find the value of the determinant 𝐴=||π‘₯βˆ’11π‘₯βˆ’1||.

  • A10π‘₯
  • Bβˆ’10π‘₯
  • Cβˆ’π‘₯
  • Dβˆ’12π‘₯
  • E12π‘₯

Q12:

Find the value of π‘₯ which satisfies ||340βˆ’250βˆ’340250||=5π‘₯βˆ’4sinsincoscos∘∘∘∘.

  • A1
  • B35
  • Cβˆ’45
  • Dβˆ’1

Q13:

Evaluate||3βˆ’415||.

Q14:

Find the value of ||βˆ’2βˆ’977||.

Q15:

Find the determinant of the matrix 5005.

Q16:

Evaluate |||10π‘₯βˆ’2π‘₯10π‘₯2π‘₯|||cossinsincos.

Q17:

Find the determinant of the following matrix. 51βˆ’15

Q18:

Find the value of |||||βˆ’1πœƒ11+πœƒβˆ’1πœƒ|||||.sincotsin

Q19:

Given that the determinant of the matrix ο”π‘Ž2𝑏5 is zero, what is 𝑏 in terms of π‘Ž?

  • A𝑏=2π‘Ž5
  • B𝑏=βˆ’2π‘Ž5
  • C𝑏=25π‘Ž
  • D𝑏=5π‘Ž2
  • E𝑏=βˆ’5π‘Ž2

Q20:

Which of the following is equal to |||βˆ’6βˆ’8πœƒ3πœƒ2|||.sinsin

  • A|||βˆ’8πœƒβˆ’623πœƒ|||sinsin
  • B|||βˆ’12πœƒβˆ’432πœƒ|||coscos
  • C|||βˆ’4βˆ’12πœƒ2πœƒ3|||coscos
  • D|||βˆ’12βˆ’42πœƒ3πœƒ2|||sinsin
  • E|||βˆ’6πœƒβˆ’432πœƒ|||coscos

Q21:

Find the determinant of the matrix 5105.

Q22:

Solve the determinant |||βˆ’πœƒπœƒπœƒπœƒ|||=βˆ’2cossincsccsc given that 0<πœƒ<90∘∘.

Q23:

Find all the possible values of π‘₯: ||1βˆ’π‘₯6βˆ’6π‘₯+1||=1.

  • A7,βˆ’7
  • B17,βˆ’17
  • C16,βˆ’16
  • D16
  • E6,βˆ’6

Q24:

Solve for π‘₯||6π‘₯βˆ’10π‘₯5π‘₯7||=||4π‘₯βˆ’10182π‘₯||.

  • Aο¬βˆ’87,βˆ’16
  • Bο¬βˆ’43,βˆ’17
  • C17,43
  • D16,87

Q25:

Solve for π‘₯: |||3π‘₯βˆ’1π‘₯+1π‘₯+13π‘₯βˆ’1|||=0.

  • Aπ‘₯=0, π‘₯=βˆ’3, or π‘₯=23
  • Bπ‘₯=βˆ’1, or π‘₯=32
  • Cπ‘₯=0, π‘₯=βˆ’13, π‘₯=1, or π‘₯=βˆ’23
  • Dπ‘₯=βˆ’1, π‘₯=32, π‘₯=βˆ’3, or π‘₯=23
  • Eπ‘₯=0, π‘₯=βˆ’3, π‘₯=βˆ’13, or π‘₯=βˆ’32

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