Finding the determinant

F

frctl

Full Member
Joined
Jun 29, 2019
Messages
252
I have the following matrix:
matrix.png

method 1
|A| = ((-18)+(-45)+(0)) - ((-12)+(0)+(0))
= (-63) - (-12)
= -51

method 2
detA = 2[-3 -3] - 3[2 -3] + 1[2 -3]
0 3 4 3 4 0
detA = 2(-9) - 3(18) + 1(-12)
detA = -18 - 54 -12
detA = -84

Which method and do I arrive at the correct answer?
 
Please check each step for yourself before asking a question.

Where did that 45 come from in the first method? One of the 0's is also wrong.

Check the -12 in the second method.

Both methods will work correctly, if you do them carefully.
 
I arrive at the inverse and transposed matrix
-9 -9 -6
-9 2 8
-12 -12 -12
Is this correct?
 
frctl said:
I arrive at the inverse and transposed matrix
-9 -9 -6
-9 2 8
-12 -12 -12
Is this correct?
Click to expand...
Hi. The matrix inverse and transpose are not the same matrix. Did you forget to post one of them?

Your result above is neither the inverse nor the transpose. Proofread, to be sure that you copied the numbers correctly onto your paperwork. Double-check your arithmetic steps, also. If you can't find mistakes, please show your work.

For checking: All of the elements in the matrix inverse are fractions, and all of those denominators are small multiples of 5. The elements in the matrix transpose are all Integers (one is zero, and two are negative).

For verification: Don't forget that a matrix times its inverse must result in the identity matrix, so that's a verification step that you can do. The verification for the transpose is that its determinant must be the same as the original matrix determinant (-60).

?
 
frctl said:
I meant the new matrix
Click to expand...
Hello. What new matrix? The matrix inverse? :confused:

Oh, I just noticed that your result in post #5 looks similar to the inverse, but with a missing scalar factor of -1/60 in front of the matrix. (That confused me.) I say "similar" because an element is incorrect in row2 and there are sign errors in row3. Please double-check your steps.

When you report a matrix that is multiplied by a scalar, don't forget to state the scalar factor! In post #5, you needed to show the scalar factor -1/60 in front of your matrix. Or, at least state in words that each matrix element needs to be multiplied by -1/60.

? It is certainly okay to complete those multiplications. For example:

In row1 col1, you have -9, and that is multiplied by -1/60.

(-1/60)(-9) = 3/20

Therefore, the inverse element R1C1 is 3/20

\(\;\)
 
Hi frctl. If you are finished with this exercise, please post your solution. Otherwise, where are you at now?

\(\;\)
 
You must log in or register to reply here.
Top