SOLUTION: What is the determinant of the matrix F and G
F=
0 3 0 0 0
a 2 b c d
e 1 f g h
i 0 j k l
m 0 n o p
and
G =
a b
Algebra ->
Matrices-and-determiminant
-> SOLUTION: What is the determinant of the matrix F and G
F=
0 3 0 0 0
a 2 b c d
e 1 f g h
i 0 j k l
m 0 n o p
and
G =
a b
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Question 1207027: What is the determinant of the matrix F and G
F=
0 3 0 0 0
a 2 b c d
e 1 f g h
i 0 j k l
m 0 n o p
and
G =
a b c d
e-a f-b g-c h-d
i-m j-n k-o l-p
m n o p
if I have matrix
M=
a b c d
e f j h
i j k l
m n o p
that has a det=|M|=5
---------------------------------
so with matrix F I took 3 as common factor and multiplied it by |M|=5 which means |F|=15
and with G I just transform it to M which would mean |G|=|M|=5
is this correct?
any help is highly appreciated
According to the cofactoring theorem for matrices and determinants,
you should take common factor -3 (= negative 3) with matrix F
and multiply it by |M| = 5, so the final determinant for matrix F is
|F| = (-3)*5 = -15.
With matrix G, your understanding is correct and the final answer is correct, too.
In the 1st row of matrix F, there are almost all zeros here.
This means it is the best choice when doing a cofactor expansion.
Circle the nonzero element of this row.
This circled element is in the 1st row and 2nd column.
Anything in this row/column combo that isn't circled is then crossed off.
I denote this as a red X
Erase those red X's.
The resulting 4x4 submatrix (temporarily ignoring the "3") is matrix M.
We will multiply 3 by this matrix determinant and stick a negative 1 out front. Recall the plus minus signs alternate like a checkerboard.
The spacing is a bit strange. I apologize. I couldn't figure out how to get it lined up perfectly.
Use the minus sign in row1,column2.
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