Q. If J = [[1, 2, 1], [0, 1, 3], [2, 1, 0]], calculate det(J). (2023)
Solution
Using the determinant formula, det(J) = 1*(1*0 - 3*1) - 2*(0*0 - 3*2) + 1*(0*1 - 1*2) = 1*(-3) - 2*(-6) + 1*(-2) = -3 + 12 - 2 = 7.
Correct Answer: A — -4
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Q. If J = [[1, 2], [2, 4]], what is det(J)? (2022)
Solution
Det(J) = (1*4) - (2*2) = 4 - 4 = 0.
Correct Answer: A — 0
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Q. If \( B = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \), what is \( |B| \)? (2022)
Solution
The determinant of \( B \) is \( 2*4 - 3*1 = 8 - 3 = 5 \).
Correct Answer: A — 5
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Q. If \( E = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \), what is \( |E| \)? (2023)
Solution
The determinant is calculated as \( 0*0 - 1*1 = 0 - 1 = -1 \).
Correct Answer: C — -1
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Q. If \( E = \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix} \), what is \( |E| \)? (2022)
Solution
The determinant is \( 1*1 - 1*1 = 1 - 1 = 0 \).
Correct Answer: A — 0
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Q. What is the determinant of F = [[2, 0], [0, 3]]? (2023)
Solution
Determinant of F = (2*3) - (0*0) = 6.
Correct Answer: D — 6
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Q. What is the determinant of G = [[1, 1, 1], [1, 2, 3], [1, 3, 6]]? (2023)
Solution
Det(G) = 1(2*6 - 3*3) - 1(1*6 - 1*3) + 1(1*3 - 1*2) = 1(12 - 9) - 1(6 - 3) + 1(3 - 2) = 3 - 3 + 1 = 1.
Correct Answer: A — 0
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Q. What is the determinant of G = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]? (2020)
Solution
Det(G) = 1(5*9 - 6*8) - 2(4*9 - 6*7) + 3(4*8 - 5*7) = 1(45 - 48) - 2(36 - 42) + 3(32 - 35) = -3 + 12 - 9 = 0.
Correct Answer: A — 0
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Q. What is the determinant of G = [[1, 2], [2, 4]]? (2020)
Solution
Determinant of G = (1*4) - (2*2) = 4 - 4 = 0.
Correct Answer: A — 0
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Q. What is the determinant of G = [[2, 1], [1, 2]]? (2021)
Solution
Det(G) = (2*2) - (1*1) = 4 - 1 = 3.
Correct Answer: B — 2
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Q. What is the determinant of G = [[2, 2], [2, 2]]? (2020)
Solution
Det(G) = (2*2) - (2*2) = 4 - 4 = 0.
Correct Answer: A — 0
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Q. What is the determinant of G = [[3, 2], [1, 4]]? (2022)
Solution
The determinant of G is (3*4) - (2*1) = 12 - 2 = 10.
Correct Answer: A — 10
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Q. What is the determinant of G = [[5, 4], [2, 3]]? (2020)
Solution
Det(G) = (5*3) - (4*2) = 15 - 8 = 7.
Correct Answer: B — 10
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Q. What is the determinant of G = [[5, 6], [7, 8]]? (2017)
Solution
Det(G) = (5*8) - (6*7) = 40 - 42 = -2.
Correct Answer: A — -2
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Q. What is the determinant of H = [[3, 1], [2, 4]]? (2023)
Solution
The determinant of H is calculated as (3*4) - (1*2) = 12 - 2 = 10.
Correct Answer: A — 10
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Q. What is the determinant of H = [[3, 2], [1, 4]]? (2020)
Solution
The determinant of H is (3*4) - (2*1) = 12 - 2 = 10.
Correct Answer: A — 10
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Q. What is the determinant of H = [[3, 2], [1, 5]]? (2021)
Solution
Determinant of H = (3*5) - (2*1) = 15 - 2 = 13.
Correct Answer: A — 7
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Q. What is the determinant of I = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]? (2015)
Q. What is the determinant of I = [[5, 6], [7, 8]]? (2020)
Solution
Determinant of I = (5*8) - (6*7) = 40 - 42 = -2.
Correct Answer: A — -2
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Q. What is the determinant of J = [[1, 2, 3], [0, 1, 4], [5, 6, 0]]? (2014)
Solution
Det(J) = 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. What is the determinant of J = [[2, 3], [4, 5]]? (2020)
Solution
The determinant of J is (2*5) - (3*4) = 10 - 12 = -2.
Correct Answer: D — 10
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Q. What is the determinant of J = [[5, 4], [2, 3]]? (2022)
Solution
The determinant of J is (5*3) - (4*2) = 15 - 8 = 7.
Correct Answer: A — 7
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Q. What is the determinant of the identity matrix I = [[1, 0], [0, 1]]? (2021)
Solution
Det(I) = (1*1) - (0*0) = 1 - 0 = 1.
Correct Answer: B — 1
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Q. What is the determinant of the matrix E = [[1, 2, 3], [0, 1, 4], [5, 6, 0]]? (2021)
Solution
The determinant of E is calculated using the rule of Sarrus or cofactor expansion, resulting in -14.
Correct Answer: A — -14
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Q. What is the determinant of the matrix G = [[2, 4], [1, 3]]? (2021)
Solution
The determinant of G is (2*3) - (4*1) = 6 - 4 = 2.
Correct Answer: A — 2
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Q. What is the determinant of the matrix J = [[2, 3], [4, 5]]? (2023)
Solution
The determinant of J is (2*5) - (3*4) = 10 - 12 = -2.
Correct Answer: A — -2
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Q. What is the determinant of the matrix J = [[5, 6], [7, 8]]? (2019)
Solution
The determinant of J is (5*8) - (6*7) = 40 - 42 = -2.
Correct Answer: A — -2
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Q. What is the determinant of the matrix \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)? (2021)
Solution
The determinant of a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is given by \( ad - bc \). Here, \( 1*4 - 2*3 = 4 - 6 = -2 \).
Correct Answer: A — -2
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Q. What is the determinant of the matrix \( C = \begin{pmatrix} 5 & 0 \\ 0 & 7 \end{pmatrix} \)? (2020)
Solution
The determinant of a diagonal matrix is the product of its diagonal elements: \( 5*7 = 35 \).
Correct Answer: A — 35
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Q. What is the determinant of the matrix \( C = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \)? (2020)
Solution
The determinant is calculated as \( 5*8 - 6*7 = 40 - 42 = -2 \).
Correct Answer: A — -2
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