What is the value of x if the matrix A = [[x, 2], [3, 4]] is singular?

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Question: What is the value of x if the matrix A = [[x, 2], [3, 4]] is singular?

Options:

Correct Answer: 3

Solution:

A matrix is singular if its determinant is zero. Det(A) = (x*4) - (2*3) = 4x - 6 = 0. Solving gives x = 1.5.

What is the value of x if the matrix A = [[x, 2], [3, 4]] is singular?

What is the value of x if the matrix A = [[x, 2], [3, 4]] is singular?

Step 1: Understand that a matrix is singular if its determinant is zero.
Step 2: Write down the formula for the determinant of a 2x2 matrix A = [[a, b], [c, d]], which is Det(A) = (a * d) - (b * c).
Step 3: Identify the values in the matrix A = [[x, 2], [3, 4]]. Here, a = x, b = 2, c = 3, and d = 4.
Step 4: Substitute the values into the determinant formula: Det(A) = (x * 4) - (2 * 3).
Step 5: Simplify the expression: Det(A) = 4x - 6.
Step 6: Set the determinant equal to zero because the matrix is singular: 4x - 6 = 0.
Step 7: Solve for x by adding 6 to both sides: 4x = 6.
Step 8: Divide both sides by 4 to find x: x = 6 / 4.
Step 9: Simplify the fraction: x = 1.5.

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