Question
Download Solution PDFGiven that the following matrix is singular: \(\left(\begin{array}{ccc} 4 & 2 x & 0 \\ 4 & 0 & 2 \\ 12 & 6 & 0 \end{array}\right)\) The value of x is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
A matrix is singular if its determinant is zero. So, we compute the determinant of the given 3×3 matrix and set it equal to 0.
\[ \text{Matrix: } \begin{bmatrix} 4 & 2x & 0 \\ 4 & 0 & 2 \\ 12 & 6 & 0 \\ \end{bmatrix} \]
Calculation:
Apply the determinant formula:
\[ \text{Det} = 4 \cdot (0 \cdot 0 - 2 \cdot 6) - 2x \cdot (4 \cdot 0 - 2 \cdot 12) + 0 \cdot (4 \cdot 6 - 0 \cdot 12) \]
\[ = 4(0 - 12) - 2x(0 - 24) + 0 = -48 + 48x \]
Set determinant = 0 (since the matrix is singular):
⇒ -48 + 48 x = 0
⇒ x =1
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