Find the determinant of a matrix

In summary, the conversation discussed finding the determinant of a matrix A and how to find the determinant of a matrix B cubed, given that the determinant of B is equal to 4. The conversation also mentioned the use of different methods, such as ninja math or the Sarus rule, to find determinants. The final answer for finding det(B^3) was determined to be 64 using the ninja math method.
  • #1
sara_87
763
0
Bonsoir everyone

can anyone confirm if i got the answer right or wrong:

Question:

find the determinant of A. A is a matrix and is equal to

1 5 -3
3 -3 3
2 13 -7

(i think you've already guessed that i don't have latex)

My answer:

i got -18


I would be grateful if anyone could confirm my answer, and if it's wrong i'll write out all the steps that i did in order to get that answer

Merci :smile:
 
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  • #2
Did you use ninja math or cofactors? I like ninja math:

[(1*-3*-7)+(5*3*2)+(3*13*-3)]-[(-3*-3*2)+(3*13*1)+(5*3*7)]=? <----- Is that -18?
 
  • #3
You're correct.
 
  • #4
According to my TI-83, that's it
 
  • #5
Thank you all so much!...(i knew i was right ;) )

and you could help me further by telling me how to find det(B^3) where det B= 4

i don't think that it's as simple as 4^3...is it?
 
  • #6
ninja math?
 
  • #7
Det is multiplicative (Det(XY)=Det(X)Det(Y)). You have been taught this. So use it.
 
  • #8
so it is 4^3, and my answer is 64
 
  • #9
Ninja math, basketweave, whatever you want to call it. You slice along the diagonals. So if you have matrix A, you would do

(A11*A22*A33+A12*A23*A31+A21*A32*A13)-(A13*A22*A31+A12*A21*A33+A23*A32*A11)
 
  • #10
Mindscrape said:
Ninja math, basketweave, whatever you want to call it. You slice along the diagonals. So if you have matrix A, you would do

(A11*A22*A33+A12*A23*A31+A21*A32*A13)-(A13*A22*A31+A12*A21*A33+A23*A32*A11)

That 'Ninja math' method is also called the Sarus rule, and it only applies for determinants of matrices of order 3.
 
  • #11
Yes I forgot to mention it is only for 3x3. Sarus rule? I did not know that. I prefer ninja math other Sarus rule though.
 

1. What is the determinant of a matrix?

The determinant of a matrix is a numerical value that can be calculated for a square matrix. It represents the scaling factor of the matrix and is used to determine important properties of the matrix, such as invertibility and the solution to a system of linear equations.

2. How is the determinant of a matrix calculated?

The determinant of a matrix can be calculated using various methods, such as cofactor expansion, row reduction, or using the properties of determinants. The most common method is cofactor expansion, which involves multiplying the elements of a chosen row or column by their corresponding cofactors and summing the results.

3. What does the determinant tell us about a matrix?

The determinant provides important information about a matrix, such as its invertibility, whether it has a unique solution to a system of linear equations, and the orientation of the matrix in space. It can also be used to find the area of a parallelogram or volume of a parallelepiped formed by the matrix's column vectors.

4. Can the determinant of a matrix be negative?

Yes, the determinant of a matrix can be negative. The sign of the determinant depends on the number of row swaps required to reduce the matrix to row-echelon form. If an odd number of row swaps are needed, the determinant will be negative. If an even number of row swaps are needed, the determinant will be positive.

5. What happens to the determinant when a matrix is multiplied by a scalar?

When a matrix is multiplied by a scalar, the determinant is also multiplied by that same scalar. In other words, the scaling factor of the matrix is also multiplied by the scalar. This property can be used to simplify the calculation of determinants, as multiplying a row or column by a constant will result in the determinant being multiplied by the same constant.

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