invertible in linear algebra?

Question

Find all numbers r such that

| 2 4 2 |
| 1 r 3 |
| 1 1 2 |

is invertible

Answer 1

A matrix is invertible if the determinant of the matrix is not =0

The determinant of a 3x3 matrix
| a b c|
| d e f | = a(ei-fh) + b(di-fg) +c(dh-eg)
| g h i |

We have a=2, b=4, c=2, d=1, e=r, f=3, g=1, h=1. i=2

So determinant
=2(2r - 3) + 4(2-3) + 2(1-r)
=4r-6 -4 +2-2r
=2r +0 = 2r

So if determinant must not =0 then 2r must not be =0

So solution for invertible matrix is r not equal to 0

Answer 2

2*(2r - 3) - 4*(2 - 3) + 2*(1 - r) must not equal zero

4r - 6 + 4 + 2 - 2r

2r must not equal zero.

r cannot be zero

Answer 3

Expand its determinant and set it equal to 0. Then solve for r. That;ll be the value for which the determinant is 0 and the matrix non-invertible.

Doug

Answer 4

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