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0 votes
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in Linear Equations by (55.0k points)
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If A = \(\begin{pmatrix} 1 & k & 3 \\ 3 & k &-2 \\ 2 & 3 & -4 \end{pmatrix}\)is singular then k = ?

((1,k,3),(3,k,-2),(2,3,-4))

A. 16/3

B. 34/3

C. 33/2

D. none of these

1 Answer

+1 vote
by (49.9k points)
selected by
 
Best answer

When a given matrix is singular then the given matrix determinant is 0. 

|A| = 0

Given,

A = \(\begin{pmatrix} 1 & k & 3 \\ 3 & k &-2 \\ 2 & 3 & -4 \end{pmatrix}\)

|A| = 0

1(-4k + 6) –k(-12 + 4) +3 (9 -2k)= 0 

-4k + 6 +12k -4k + 27 -6k = 0 

-2k +33 = 0

k = 33/2,

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