SOLUTION: A matrix is given- [ 2k-1 3 3 3 2k-1 3 3 3 2k-1 ] Find value of k when matrix is singular.

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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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