Matrix inversion

[dumbledore]

Determine all values of k for which A is invertible.

A=

1 -5 1
-1 6 k
-3 14 -6

I re-wrote as

1 -5 1 | 1 0 0
-1 6 k | 0 1 0
-3 14 -6 | 0 0 1

then performed r2-> r2 + r1, r3-> r3 + 3r1, r3-> r3 + r2

and got k cannot = 2 for A to be invertible. Is that the correct answer and correct method?

 

[mmm4444bot]

Yes -- your answer is correct.

Your row operations are one method; calculating the Determinant of A is another.

If the exercise instructions do not specify a method, then you're free to choose the "correct" method. Cheers :cool:

 

[dumbledore]

Yes -- your answer is correct.

Your row operations are one method; calculating the Determinant of A is another.

If the exercise instructions do not specify a method, then you're free to choose the "correct" method. Cheers :cool:

Thanks for the response. I have yet to learn the determinant method. So I must have used the correct method.