SOLUTION: Find the determinant for matrix [2 -1 -3, 1, 0 2, -1 2 1]
One of the following is the correct answer. Which one?
A) 5
B) 17
C) 18
D) -14
E) -11
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Matrices-and-determiminant
-> SOLUTION: Find the determinant for matrix [2 -1 -3, 1, 0 2, -1 2 1]
One of the following is the correct answer. Which one?
A) 5
B) 17
C) 18
D) -14
E) -11
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Question 1198436: Find the determinant for matrix [2 -1 -3, 1, 0 2, -1 2 1]
One of the following is the correct answer. Which one?
A) 5
B) 17
C) 18
D) -14
E) -11
Copy the first two columns to place it to the right of the vertical bar like so
Then highlight these diagonals in red
Multiply everything in each diagonal separately
A = 1st diagonal = 2*0*1 = 0
B = 2nd diagonal = -1*2*(-1) = 2
C = 3rd diagonal = -3*1*2 = -6
Afterward you would add up the products
D = A+B+C = 0+2+(-6) = -4
We'll use this value later.
Repeat the same idea for these diagonals highlighted in blue.
Multiply everything in each diagonal separately
E = 1st diagonal = -1*0*(-3) = 0
F = 2nd diagonal = 2*2*2 = 8
G = 3rd diagonal = 1*1*(-1) = -1
Then add up the products
H = E+F+G = 0 + 8 + (-1) = 7
The last step is to subtract the results of D and H to arrive at the determinant value.
Determinant of 3x3 matrix = D - H = -4 - 7 = -11
Side note: the entire process shown above applies to 3x3 matrices only.
As an alternate method to compute the determinant, you can use a cofactor expansion.
You can use a tool like WolframAlpha or GeoGebra (both of which are free) to verify the answer.
There are many other free online matrix determinant calculators out there.
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