Matrices & Determinants

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Q1. What is the determinant of G = [[1, 2], [2, 4]]? (2020)

Solution:

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

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Q2. Find the determinant of the matrix D = [[3, 2, 1], [1, 0, 2], [2, 1, 3]]. (2020)

Solution:

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

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Q3. What is the determinant of G = [[3, 2], [1, 4]]? (2022)

Solution:

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

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Q4. Calculate the determinant of D = [[3, 2, 1], [1, 0, 2], [2, 1, 3]]. (2020)

Solution:

Det(D) = 3(0*3 - 2*1) - 2(1*3 - 2*2) + 1(1*1 - 0*2) = 3(0 - 2) - 2(3 - 4) + 1(1) = -6 + 2 + 1 = -3.

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Q5. What is the determinant of G = [[2, 1], [1, 2]]? (2021)

Solution:

Det(G) = (2*2) - (1*1) = 4 - 1 = 3.

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Q6. Find the determinant of J = [[5, 2], [1, 3]]. (2020)

Solution:

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

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Q7. For the matrix E = [[1, 2], [2, 4]], what is the determinant? (2021)

Solution:

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

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Q8. Find the determinant of \( G = \begin{pmatrix} 4 & 2 \\ 3 & 1 \end{pmatrix} \). (2020)

Solution:

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

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Q9. Find the determinant of E = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]. (2019)

Solution:

Determinant of E = 0 (rows are linearly dependent).

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Q10. What is the determinant of the matrix \( F = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \)? (2020)

Solution:

The determinant is 0 because the rows are linearly dependent.