Which of the following is a singular matrix? (2019)

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Question: Which of the following is a singular matrix? (2019)

Options:

Correct Answer: [[2, 3], [4, 6]]

Exam Year: 2019

Solution:

A singular matrix is one that does not have an inverse, which occurs when its determinant is zero. The matrix [[2, 3], [4, 6]] is singular.

Which of the following is a singular matrix? (2019)

Which of the following is a singular matrix? (2019)

Step 1: Understand what a matrix is. A matrix is a rectangular array of numbers.
Step 2: Learn about the determinant of a matrix. The determinant is a special number that can be calculated from a square matrix.
Step 3: Know that a singular matrix is a matrix that does not have an inverse.
Step 4: Remember that a matrix is singular if its determinant is equal to zero.
Step 5: Look at the given matrix [[2, 3], [4, 6]].
Step 6: Calculate the determinant of the matrix. For a 2x2 matrix [[a, b], [c, d]], the determinant is calculated as (a * d) - (b * c).
Step 7: For the matrix [[2, 3], [4, 6]], calculate the determinant: (2 * 6) - (3 * 4) = 12 - 12 = 0.
Step 8: Since the determinant is 0, the matrix [[2, 3], [4, 6]] is a singular matrix.

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