If the determinant | x 2 | | 3 4 | = 0, find x.

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Question: If the determinant | x 2 | | 3 4 | = 0, find x.

Options:

Correct Answer: 2

Solution:

Setting the determinant to zero gives x*4 - 2*3 = 0, thus x = 1.5.

If the determinant | x 2 | | 3 4 | = 0, find x.

If the determinant | x 2 | | 3 4 | = 0, find x.

Correct Answer: 1.5

Step 1: Write down the determinant formula for a 2x2 matrix. The formula is | a b | | c d | = a*d - b*c.
Step 2: Identify the values in the matrix: a = x, b = 2, c = 3, d = 4.
Step 3: Substitute the values into the determinant formula: | x 2 | | 3 4 | = x*4 - 2*3.
Step 4: Set the determinant equal to zero: x*4 - 2*3 = 0.
Step 5: Calculate 2*3, which equals 6. Now the equation is x*4 - 6 = 0.
Step 6: Add 6 to both sides of the equation: x*4 = 6.
Step 7: Divide both sides by 4 to solve for x: x = 6/4.
Step 8: Simplify 6/4 to get x = 1.5.

Determinants – Understanding how to calculate the determinant of a 2x2 matrix and setting it to zero to find values of variables.
Solving Linear Equations – Applying algebraic manipulation to solve for the variable in the equation derived from the determinant.