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Question 934861: A matrix is given-
[ 2k-1 3 3
3 2k-1 3
3 3 2k-1 ]
Find value of k when matrix is singular.
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! A matrix is given-
Find value of k when matrix is singular.
A matrix is non-invertable, or singular, when its determinant is zero; so, find its determinant in terms of  , then set that to  and solve for .
here, determinant is  , then we have
 ....solve for
 => then we have 
plug this value in given matrix
check if determinant is equal to zero
| Solved by pluggable solver: Finding the Determinant of a 3x3 Matrix |
If you have the general 3x3 matrix:
the determinant is: 
Which further breaks down to:
Note:  ,  and  are determinants themselves.
If you need help finding the determinant of 2x2 matrices (which is required to find the determinant of 3x3 matrices), check out this solver
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From the matrix , we can see that  ,  ,  ,  ,  ,  ,  ,  , and 
Start with the general 3x3 determinant.
 Plug in the given values (see above)
 Multiply
 Subtract
 Multiply
 Combine like terms.
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Answer:
So , which means that the determinant of the matrix is 0
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