anonymous
  • anonymous
Evaluate the determinant of the matrix [8. 3 -2] [-1 3 2] [ 5 -1 1]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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DanJS
  • DanJS
scalar triple product
anonymous
  • anonymous
what?
UsukiDoll
  • UsukiDoll
cofactor expansion... that's needed to shrink the matrix down to a 2 x 2

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More answers

DanJS
  • DanJS
A * (B x C)
anonymous
  • anonymous
How?
DanJS
  • DanJS
do you know a 2 by 2 determinant?
anonymous
  • anonymous
yes! i just don't know how to find the determinant for a 3x3 matrix
DanJS
  • DanJS
Determinant of 2 by 2 matrix = a*d - cd [a b] [c d]
DanJS
  • DanJS
ok...
UsukiDoll
  • UsukiDoll
ad - bc for determinant of a 2 x 2 matrix for a 3 x 3 matrix we have to use cofactor expansion.
anonymous
  • anonymous
how do i do cofactor expansion?
DanJS
  • DanJS
|dw:1438052983671:dw|
UsukiDoll
  • UsukiDoll
Cofactor expansion expanding a row ... find the minors and the cofactors of the first row entries ( you can choose second row or third row entries but the sign pattern is different).
DanJS
  • DanJS
|dw:1438053078307:dw|
DanJS
  • DanJS
Cover first column, 8*det of that 2x2 is the first of 3 terms
DanJS
  • DanJS
look up determinant of 3 x 3 matrix.. lol this is alot of drawing
UsukiDoll
  • UsukiDoll
the signs for the 3 x 3 matrix is like a checkerboard |dw:1438053171537:dw| that's why I use the first drawing a lot.
UsukiDoll
  • UsukiDoll
* first row signs
DanJS
  • DanJS
yeah i just remember the second is minus
UsukiDoll
  • UsukiDoll
|dw:1438053270643:dw|
UsukiDoll
  • UsukiDoll
cut row one cut column one cut row one cut column two cut row one cut column three
UsukiDoll
  • UsukiDoll
|dw:1438053376916:dw|
UsukiDoll
  • UsukiDoll
ok I'm going to clean this up a bit.. but where I circled the row and column... you draw a line to cross them out... you should be left with 4 numbers... that's your 2 x 2 matrix. now you can take the determinant of those matrices...
UsukiDoll
  • UsukiDoll
|dw:1438053458361:dw|
UsukiDoll
  • UsukiDoll
|dw:1438053534643:dw|
UsukiDoll
  • UsukiDoll
|dw:1438053599579:dw| normally we would have a + sign but that negative -2 on the first row third column entry changes that.
UsukiDoll
  • UsukiDoll
|dw:1438053728550:dw| so we should have this equation after we have done cofactor expansion. Now we can take the determinant of the 2 x 2 matrix and combine like terms. The final answer for the determinant of the 3 x 3 matrix should be just a single number

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