Matrices & Determinants for Competitive Exam Success

Matrices & Determinants

Q. Find the determinant of F = [[4, 3], [2, 1]]. (2018)

A. -2
B. 2
C. 6
D. 8

Solution

Det(F) = (4*1) - (3*2) = 4 - 6 = -2.

Correct Answer: A — -2

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Q. Find the determinant of F = [[4, 5], [6, 7]]. (2020)

A. -2
B. 2
C. 10
D. 12

Solution

Det(F) = (4*7) - (5*6) = 28 - 30 = -2.

Correct Answer: A — -2

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Q. Find the determinant of G = [[1, 2], [2, 4]]. (2020)

A. 0
B. 1
C. 2
D. 4

Solution

Determinant of G = (1*4) - (2*2) = 4 - 4 = 0.

Correct Answer: A — 0

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Q. Find the determinant of H = [[3, 1], [2, 5]]. (2021)

A. 7
B. 8
C. 6
D. 5

Solution

Determinant of H = (3*5) - (1*2) = 15 - 2 = 13.

Correct Answer: A — 7

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Q. Find the determinant of J = [[5, 2], [1, 3]]. (2020)

A. 10
B. 11
C. 12
D. 13

Solution

The determinant of J is calculated as (5*3) - (2*1) = 15 - 2 = 13.

Correct Answer: A — 10

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Q. Find the determinant of the matrix D = [[3, 2, 1], [1, 0, 2], [2, 1, 3]]. (2020)

A. 0
B. 1
C. 2
D. 3

Solution

The determinant of D can be calculated using the rule of Sarrus or cofactor expansion, which results in 0.

Correct Answer: A — 0

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Q. Find the determinant of the matrix D = [[4, 2], [3, 1]]. (2023)

A. -2
B. 2
C. 10
D. 12

Solution

The determinant of D is calculated as (4*1) - (2*3) = 4 - 6 = -2.

Correct Answer: A — -2

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Q. Find the determinant of the matrix \( E = \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \). (2021)

A. 10
B. 14
C. 5
D. 6

Solution

The determinant is \( 3*4 - 2*1 = 12 - 2 = 10 \).

Correct Answer: A — 10

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Q. Find the determinant of the matrix \( J = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \). (2022)

A. 1
B. 2
C. 3
D. 4

Solution

The determinant is \( 2*7 - 3*5 = 14 - 15 = -1 \).

Correct Answer: A — 1

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Q. Find the determinant of \( G = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \). (2021)

A. 1
B. 2
C. 3
D. 4

Solution

The determinant is calculated as \( 2*7 - 3*5 = 14 - 15 = -1 \).

Correct Answer: A — 1

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Q. Find the determinant of \( G = \begin{pmatrix} 4 & 2 \\ 3 & 1 \end{pmatrix} \). (2020)

A. -2
B. 2
C. 0
D. 1

Solution

The determinant is \( 4*1 - 2*3 = 4 - 6 = -2 \).

Correct Answer: A — -2

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Q. Find the value of \( x \) if \( \begin{vmatrix} 1 & 2 \\ 3 & x \end{vmatrix} = 0 \). (2023)

A. 1
B. 2
C. 3
D. 4

Solution

Setting the determinant to zero: \( 1*x - 2*3 = 0 \) gives \( x - 6 = 0 \) or \( x = 6 \).

Correct Answer: C — 3

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Q. For the matrix E = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], find det(E). (2021)

A. -24
B. 24
C. 0
D. 12

Solution

Using the determinant formula, det(E) = 1*(1*0 - 4*6) - 2*(0*0 - 4*5) + 3*(0*6 - 1*5) = 1*(-24) - 2*(-20) - 15 = -24 + 40 - 15 = 1.

Correct Answer: A — -24

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Q. For the matrix E = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], find the determinant. (2023)

A. -24
B. 24
C. 0
D. 12

Solution

Determinant of E = 1(1*0 - 4*6) - 2(0*0 - 4*5) + 3(0*6 - 1*5) = 1(0 - 24) - 2(0 - 20) + 3(0 - 5) = -24 + 40 - 15 = 1.

Correct Answer: A — -24

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Q. For the matrix E = [[1, 2], [2, 4]], what is the determinant? (2021)

A. 0
B. 1
C. 2
D. 4

Solution

Determinant of E = (1*4) - (2*2) = 4 - 4 = 0.

Correct Answer: A — 0

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Q. If C = [[0, 1], [1, 0]], what is det(C)? (2022)

A. 0
B. 1
C. -1
D. 2

Solution

Determinant of C = (0*0) - (1*1) = 0 - 1 = -1.

Correct Answer: C — -1

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Q. If E = [[2, 1, 3], [1, 0, 2], [4, 1, 1]], what is det(E)? (2020)

A. -1
B. 0
C. 1
D. 2

Solution

The determinant of E can be calculated using the rule of Sarrus or cofactor expansion, resulting in 0.

Correct Answer: A — -1

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Q. If E = [[a, b], [c, d]], what is the expression for det(E)? (2023)

A. ad - bc
B. ab + cd
C. ac - bd
D. bc - ad

Solution

The determinant of E is calculated as (a*d) - (b*c) = ad - bc.

Correct Answer: A — ad - bc

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Q. If F = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], what is det(F)? (2021)

A. -14
B. 14
C. 0
D. 10

Solution

Det(F) = 1(1*0 - 4*6) - 2(0*0 - 4*5) + 3(0*6 - 1*5) = 1(0 - 24) - 2(0 - 20) + 3(0 - 5) = -24 + 40 - 15 = 1.

Correct Answer: A — -14

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Q. If F = [[2, 0], [0, 3]], what is det(F)? (2020)

A. 0
B. 6
C. 5
D. 2

Solution

The determinant of F is calculated as (2*3) - (0*0) = 6.

Correct Answer: B — 6

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Q. If F = [[2, 1, 3], [1, 0, 2], [0, 1, 1]], what is det(F)? (2023)

A. 1
B. 2
C. 3
D. 4

Solution

Det(F) = 2(0*1 - 2*1) - 1(1*1 - 2*0) + 3(1*1 - 0*0) = 2(0 - 2) - 1(1) + 3(1) = -4 - 1 + 3 = -2.

Correct Answer: C — 3

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Q. If F = [[2, 1, 3], [1, 0, 2], [3, 1, 1]], find det(F). (2022)

A. -4
B. 4
C. 0
D. 8

Solution

Using the determinant formula, det(F) = 2(0*1 - 2*1) - 1(1*1 - 2*3) + 3(1*1 - 0*3) = 2(0 - 2) - 1(1 - 6) + 3(1 - 0) = -4 + 5 + 3 = 4.

Correct Answer: A — -4

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Q. If F = [[2, 1, 3], [1, 0, 2], [3, 4, 1]], find det(F). (2022)

A. -10
B. 10
C. 0
D. 5

Solution

Using the determinant formula, det(F) = 2*(0*1 - 2*4) - 1*(1*1 - 2*3) + 3*(1*4 - 0*3) = 2*(-8) - 1*(-5) + 3*4 = -16 + 5 + 12 = 1.

Correct Answer: A — -10

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Q. If F = [[2, 1], [1, 3]], what is the value of det(F)? (2022)

A. 5
B. 6
C. 7
D. 8

Solution

The determinant of F is (2*3) - (1*1) = 6 - 1 = 5.

Correct Answer: A — 5

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Q. If G = [[1, 1], [1, -1]], find det(G). (2022)

A. 0
B. 1
C. -1
D. 2

Solution

Determinant of G = (1*-1) - (1*1) = -1 - 1 = -2.

Correct Answer: B — 1

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Q. If H = [[1, 1], [1, -1]], find det(H). (2016)

A. 0
B. 1
C. -1
D. 2

Solution

Det(H) = (1*-1) - (1*1) = -1 - 1 = -2.

Correct Answer: B — 1

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Q. If H = [[1, 2, 1], [0, 1, 0], [2, 1, 1]], find det(H). (2021)

A. 0
B. 1
C. 2
D. 3

Solution

The determinant of H is calculated as 1(1*1 - 0*1) - 2(0*1 - 0*2) + 1(0*1 - 1*2) = 1 - 0 - 2 = -1.

Correct Answer: B — 1

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Q. If H = [[1, 2], [2, 4]], what is det(H)? (2020)

A. 0
B. 1
C. 2
D. 3

Solution

The determinant of H is (1*4) - (2*2) = 4 - 4 = 0.

Correct Answer: A — 0

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Q. If H = [[2, 3], [4, 5]], find det(H). (2022)

A. -2
B. 1
C. 2
D. 7

Solution

Det(H) = (2*5) - (3*4) = 10 - 12 = -2.

Correct Answer: D — 7

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Q. If H = [[2, 3], [4, 5]], what is det(H)? (2022)

A. -2
B. 2
C. 7
D. 1

Solution

Det(H) = (2*5) - (3*4) = 10 - 12 = -2.

Correct Answer: A — -2

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Showing 31 to 60 of 112 (4 Pages)

Matrices & Determinants

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