Question
Download Solution PDFFor how many values of k, is the matrix \(\left[ {\begin{array}{*{20}{c}} 0&{\rm{k}}&4\\ { - {\rm{k}}}&0&{ - 5}\\ { - {\rm{k}}}&{\rm{k}}&{ - 1} \end{array}} \right]\) singular?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The matrix is singular if |A| = 0
Calculations:
Given the matrix \(\left[ {\begin{array}{*{20}{c}} 0&{\rm{k}}&4\\ { - {\rm{k}}}&0&{ - 5}\\ { - {\rm{k}}}&{\rm{k}}&{ - 1} \end{array}} \right]\) singular
We know that the matrix is singular iff |A| = 0
⇒\(\rm\begin{vmatrix} 0 &k &4 \\ -k &0 &-5 \\ -k &k &-1 \end{vmatrix} = 0\)
⇒ 0 - k (k - 5k) + 4 (- k2) = 0
⇒ 4k2 - 4k2 = 0
Therefore, we can take any value of k it makes the matrix singular.
Hence the total value of k is infinite.
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