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

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

Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52790) (Show Source): You can put this solution on YOUR website!
.

Use the definition of the determinant and make all necessary calculations on your own.

It is not a job for a tutor.

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Original matrix determinant

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.

-------------------------------------

Answer: -11 (choice E)

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