Find the value of \( x \) if \( \begin{vmatrix} 1 & 2 \\ 3 & x \end{vmat

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Question: Find the value of \\( x \\) if \\( \\begin{vmatrix} 1 & 2 \\\\ 3 & x \\end{vmatrix} = 0 \\). (2023)

Options:

Correct Answer: 3

Exam Year: 2023

Solution:

Setting the determinant to zero: \\( 1*x - 2*3 = 0 \\) gives \\( x - 6 = 0 \\) or \\( x = 6 \\).

Find the value of \( x \) if \( \begin{vmatrix} 1 & 2 \\ 3 & x \end{vmatrix} = 0 \). (2023)

Find the value of \( x \) if \( \begin{vmatrix} 1 & 2 \\ 3 & x \end{vmatrix} = 0 \). (2023)

Step 1: Understand that we need to find the value of x in the determinant of a 2x2 matrix.
Step 2: Write down the determinant formula for a 2x2 matrix: If the matrix is \( \begin{vmatrix} a & b \ \ c & d \end{vmatrix} \), the determinant is calculated as \( ad - bc \).
Step 3: Identify the values from the given matrix \( \begin{vmatrix} 1 & 2 \ \ 3 & x \end{vmatrix} \): Here, a = 1, b = 2, c = 3, and d = x.
Step 4: Substitute the values into the determinant formula: \( 1*x - 2*3 \).
Step 5: Simplify the expression: This becomes \( x - 6 \).
Step 6: Set the determinant equal to zero: \( x - 6 = 0 \).
Step 7: Solve for x by adding 6 to both sides: \( x = 6 \).

Determinants – Understanding how to calculate the determinant of a 2x2 matrix and setting it to zero to find values of variables.
Linear Algebra – Application of linear algebra concepts to solve for unknowns in matrix equations.