Question

Suppose the square matrix
C={1 1 -1}
3 0 -1
-1 -1 2
1) Evaluate det(C) by expanding along the first row, Include steps of the calculation. NO MARKS awarded if any other method is used.

Answer 1

Do you know how to calculate determinant ??

Answer 2

Yes I do, but I don't understand what the expand along the first row means.

Answer 3

Using first row...

Tell me how you calculate determinant??

Calculate the determinant for this by what ever the way you know ..

Answer 4

Using first row means you will use :

1 1 and -1 for calculating the determinant..

I will show you in general what do you get using first row for determinant ..

Answer 5

I'm sorry Waterineyes, but I don't understand why you minused the b part of the equation, was that an error or it's the way it is.

Answer 6

No it is not the error..

Answer 7

Generally there are sign given to all the positions of matrix..

Answer 8

Oh thanks a lot, I think I understand now, let me try doing the exercise... Will be back in 2 minutes...

Answer 9

Take your time..

Answer 10

One more thing, do we consider all the signs when doing the exercise? because I've got 2 different answers, in 1 I didn't consider the signs and the second 1 I considered the signs. I then got 9 and 8.

Answer 11

Can you show how you got them so that I can find out the mistake or I can see them with my eyes..??

Answer 12

No, when expanding along first row, you will use the signs of first row only..

For example : a and c will be positive and b will be negative..

Do not use the signs for other values like d e f g h i..

Leave these values as such...

Use the signs for a b and c only..

Answer 13

See here :

Det(C) = \(1(0 \cdot2 - (-1) \cdot (-1) - 1 (3 \cdot 2 - (-1) \cdot (-1) + -1(3 \cdot (-1) - (-1) \cdot 0))\)

Answer 14

Simplifying little bit you will get like this :

Det(C) = \(1(-1) - 1(5) - 1(-3)\)

Solve this to get the determinant..