SOLUTION: B= 1 2 3 2 5 3 1 0 8 Find the inverse of Matrix B. Answer: Det(M)= 40-26-15 = -1 M11= 40 M21= 13 M31=-5 M12=16 M22=5 M32=-2 M13=-9 M23=-3 M33=1

Algebra ->  Matrices-and-determiminant -> SOLUTION: B= 1 2 3 2 5 3 1 0 8 Find the inverse of Matrix B. Answer: Det(M)= 40-26-15 = -1 M11= 40 M21= 13 M31=-5 M12=16 M22=5 M32=-2 M13=-9 M23=-3 M33=1      Log On


   

Question 950149: B=
1 2 3
2 5 3
1 0 8
Find the inverse of Matrix B.
Answer:
Det(M)=
40-26-15
= -1

M11= 40
M21= 13
M31=-5
M12=16
M22=5
M32=-2
M13=-9
M23=-3
M33=1
40 16 -9
13 5 -3
-5 -2 1
+ - +
- + -
+ - +
40 -16 -9
-13 5 3
-5 2 1
M^-1=1/-1
Brackets
-40 16 9
13 -5 -3
5 -2 -1
Brackets
Did I do it right? Thanks in advance.




Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

yes, you did it right


%28matrix%283%2C3%2C1%2C2%2C3%2C2%2C+5+%2C3%2C1%2C0%2C8%29%29

inverse
%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29

Solved by pluggable solver: Finding the Determinant of a 3x3 Matrix

If you have the general 3x3 matrix:

%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29

the determinant is:

Which further breaks down to:



Note: abs%28matrix%282%2C2%2Ce%2Cf%2Ch%2Ci%29%29, abs%28matrix%282%2C2%2Cd%2Cf%2Cg%2Ci%29%29 and abs%28matrix%282%2C2%2Cd%2Ce%2Cg%2Ch%29%29 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 %28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29, we can see that a=-40, b=16, c=9, d=13, e=-5, f=-3, g=5, h=-2, and i=-1

Start with the general 3x3 determinant.

Plug in the given values (see above)

Multiply

Subtract

abs%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29=40-32%2B-9 Multiply

abs%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29=-1 Combine like terms.


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Answer:

So abs%28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29=-1, which means that the determinant of the matrix %28matrix%283%2C3%2C-40%2C16%2C9%2C13%2C-5%2C-3%2C5%2C-2%2C-1%29%29 is -1