- #1

- 86

- 0

Hello!

Please, help me to see my mistake - for quite a while I can't solve a very easy matrix.

I have to

find the inverse of the given matrix using their determinants and adjoints.

4 6 -3

3 4 -3

1 2 6

to find adjoint matrix I need to find cofactors 11, 12, etc till 33.

Cofactor11 = (-1)^(1+1) x det([4 -3] => C11 = 24 + 6 = 30

2 6

Cofactor12 = (-1)^(1+2) x det([3 -3] => C12 = -(18 + 3) = -21

1 6

Cofactor13 = (-1)^(1+3) x det([3 4] => C13 = 6 - 4 = 2

1 2

Cofactor21 = (-1)^(2+1) x det([6 -3] => C21 = -(36 + 6) = -42

2 6

Cofactor22 = (-1)^(2+2) x det([4 -3] => C22 = 24 + 3 = 27

1 6

Cofactor23 = (-1)^(2+3) x det([4 6] => C23 = -(8 - 6) = -2

1 2

Cofactor31 = (-1)^(3+1) x det([6 -3] => C31 = -6

4 -3

Cofactor32 = (-1)^(3+2) x det([4 -3] => C32 = -(-12 + 9) = 3

3 -3

Cofactor33 = (-1)^(3+3) x det([4 6] => C33 = 16 - 18 = -2

3 4

Adjoint matrix:

30 -42 -6

-21 27 3

2 -2 -2

det(of initial matrix taken by the first row) = 4 x (-1)^(1+1) x det([A11)] + 6 x (-1)^(1+2) x det([A12)] + (-3) x (-1)^(1+3) x det([A13)] = 4 x 30 + 6 x (-21) + (-3) x (-2) = 0

and if I try to find the det of intial matrix by expanding over the third row I get 1 x (-6) + 2 x (-1) x (-3) + 6 x (-2) = -2

and if I try to find the det of intial matrix by expanding over the second row I get (-3) x 42 + 4 x 27 + 3 x 2 = -12

I have tried multiple times, with different rows for initial matrix, and each time I get a different result.

Am I doing something wrong with cofactors?

Thank you!

Please, help me to see my mistake - for quite a while I can't solve a very easy matrix.

I have to

find the inverse of the given matrix using their determinants and adjoints.

4 6 -3

3 4 -3

1 2 6

to find adjoint matrix I need to find cofactors 11, 12, etc till 33.

Cofactor11 = (-1)^(1+1) x det([4 -3] => C11 = 24 + 6 = 30

2 6

Cofactor12 = (-1)^(1+2) x det([3 -3] => C12 = -(18 + 3) = -21

1 6

Cofactor13 = (-1)^(1+3) x det([3 4] => C13 = 6 - 4 = 2

1 2

Cofactor21 = (-1)^(2+1) x det([6 -3] => C21 = -(36 + 6) = -42

2 6

Cofactor22 = (-1)^(2+2) x det([4 -3] => C22 = 24 + 3 = 27

1 6

Cofactor23 = (-1)^(2+3) x det([4 6] => C23 = -(8 - 6) = -2

1 2

Cofactor31 = (-1)^(3+1) x det([6 -3] => C31 = -6

4 -3

Cofactor32 = (-1)^(3+2) x det([4 -3] => C32 = -(-12 + 9) = 3

3 -3

Cofactor33 = (-1)^(3+3) x det([4 6] => C33 = 16 - 18 = -2

3 4

Adjoint matrix:

30 -42 -6

-21 27 3

2 -2 -2

det(of initial matrix taken by the first row) = 4 x (-1)^(1+1) x det([A11)] + 6 x (-1)^(1+2) x det([A12)] + (-3) x (-1)^(1+3) x det([A13)] = 4 x 30 + 6 x (-21) + (-3) x (-2) = 0

and if I try to find the det of intial matrix by expanding over the third row I get 1 x (-6) + 2 x (-1) x (-3) + 6 x (-2) = -2

and if I try to find the det of intial matrix by expanding over the second row I get (-3) x 42 + 4 x 27 + 3 x 2 = -12

I have tried multiple times, with different rows for initial matrix, and each time I get a different result.

Am I doing something wrong with cofactors?

Thank you!

Last edited: