Practice Determinants (21.3.5) - Linear Algebra - Mathematics (Civil Engineering -1)

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6 sample questions

Question 1.
Calculate the determinant of the matrix [[2, 3], [1, 4]].
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Use the formula: ad - bc for a 2x2 matrix.
Question 2.
Is the matrix [[0, 0], [0, 0]] singular or non-singular?
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Check if the determinant is zero.
3Question 3.
What is the determinant of a matrix A = [[1, 2], [3, 4]]?
- -2
- 0
- 2
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Use the formula for a 2x2 matrix.
4Question 4.
True or False: If det(A) = 0, then A is invertible.
- True
- False
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Think about the meaning of a singular matrix.
Question 5.
Given a 3x3 matrix A where A = [[2, -1, 3], [1, 0, 4], [0, 1, 5]], compute the determinant and interpret its significance.
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Use the cofactor expansion method for 3x3 matrices.
Question 6.
Consider two matrices A and B where det(A) = 6 and det(B) = 2. What is the determinant of the inverse of matrix A and the product of A and B?
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Review properties of determinants for inverses and products.

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