# determinants

1. ### Determinants

Hello. I have some problem with a question. Let g be a given function of two variables and h be a given function of one variable. Let u = f(x,y) = h(g(x,y) and v = g(x,y). Calculate: d(u,v) / d(x,y) How should i interpret this question? Would be pleased if someone could give me a...
2. ### Determinant (without expansion)

Can anyone help me with this (Worried) Evaluate using the properties, x+y y+z z+x z x y 2 2 2 for example - Column 1 tends to Column 1 - Column 2, Row 3 tends to Row 3 - 2 X Row 1...
3. ### Determinants

How to do question 36?
4. ### using determinants to prove invertible matrices

Could really use some help. I'm getting lost in all of the notation Let A∈Cn×n, let det(λIn−A)=λn+∑k=0n−1akλk denote the characteristic polynomial of A. Prove that if A is invertible, then A−1=−1a0[An−1+∑k=1n−1akAk−1]
5. ### Determinants: What is the motivation?

The name 'determinant' implies that it determines. It determines the value of variable x3 by calculating its coefficient in the linear system of equations say, a1x1 + a2x2 + a3x3 = c1; a4x1 + a5x2 + a6x3 = c2; a7x1 + a8x2 + a9x3 = c3; using Gauss-elimination, where a1 through a9 are constants...
6. ### Determinants and complex numbers

Hey everyone, Do you know if there are any links between the property of matrix determinants and Complex numbers. - a complex number being z=x+yi, where x and y are real numbers and i is the imaginary number which represents sqrt(-1) - a matrix being a 2x2 representation of a...
7. ### Determinants as scalings factors and cross products

In two dimensions, it is easy to explain why the determinant of a linear transformation works as a scaling factor of parallellograms, by showing that the formula is the same as the cross product. Likewise, for three dimensions, the determinant could be shown to be a scaling factor by showing...

Question 1: Let A be a k x k matrix and let B be an (n-k) x (n-k) matrix. Let E= \begin{array}{cc} I_k & 0 \\ 0 & B\end{array} Show that det(E) = det(B) My attempt: det(E)=det(BI_k) - det(00)=det(B)det(I_k)=det(B)*1=det(B) I'm not sure this is correct, as I don't know the rules for finding...
9. ### Basic determinants

Need help with some basic determinants ( atleast I think thats basic stuff ). I know I must create Determinant from first, but im not sure how - do I need to take those free numbers behind equal sign? Second goes by determinant properties, but evrything I tryed didnt work. Please help me as...
10. ### Solving Linear Eqaution using Minors, cofactors, and determinants

Im pretty much confused on how to solve this, x + y = 6 2x + y = 9 Can you give me a step by step answer?
11. ### a question involving the determinant...

given: A = |a b c| |d e f| det(A) = 5 |g h i| B = |a u c| |d v f| det(B) = -3 |g w i| FIND: |-3a c 2b - u| |-3d f 2e - v| |-3g i 2h - w| -it's pretty much "B" except with the column of A in it...not sure what to do...
12. ### Determinants

What is the best way to describe to a non math person what a determinant is and its possible uses?
13. ### determinants !

Find the determinants of the following matrices a) u= 1 2 answear i got is -13 3 4 w= 6 7 answear i got is -1 7 8 a = 0 3 -1 answear i got is 1 0 2 -1 1 1 1 B = 0 1 2 answear i got is -6 1 0 2 2 2 2...
14. ### A quick question in determinants

Let A be a real 101x101 matrix. If A is anti-symmetric, then |A^1001 + A^1003|= 0. Why is this true? This was the correct answer to a multiple-choice question.
15. ### Determinants (using elementary row operations)

Hi, if anyone could explain how you get from (x+y+z+t)det 1 1 1 1 qqqqqqqqqqq y z t x qqqqqqqqqqq z t x y qqqqqqqqqqq t x y z to (x+y+z+t)det 0 1 1 1 qqqqqqqqqq (y-z+t-x) z t x qqqqqqqqqq (z-t+x-y) t x y qqqqqqqqqq (t-x+y-z) x y z that would be brilliant! Totally...
16. ### Systemof linear equations (determinants)- tricky word problem

A mail-order company charges $4 for shipping orders of less than$50, $6 for orders from$50- $200, and$8 for orders over $200. One day the total shipping charges were$2160 for 384 orders. Find the number of orders shipped at each rate if the number of orders under \$50 is 12 more than twice...
17. ### The importance of determinants in linear algebra.

In some literature on linear algebra determinants play a critical role and are emphasized in the earlier chapters. (See books by Anton & Rorres, and Lay). However in other literature it is totally ignored until the latter chapters. (See Gilbert Strang). How much importance should we give the...
18. ### Determinants of this matrix - pls help

Hi, can someone help me out with this, how do I solve this matrix question: Let A = [a,b,c; d,e,f; g,h,i] Given that detA= alpha and alpha is not equal to zero, express each of the following terms of alpha: a) det(2A) b) det(A^-1) c) det [2a,2b,2c; d,e,f; g,h,i] d) det [a,b,c; d,e,f...
19. ### Eigenvalues without using determinants

Hello I had a linear algebra teacher (a long time ago) who said there was a simpler way to obtain eigenvalues, without using determinants. I wonder what that method is. Can anyone point me to a book where I can find it? Thank you.
20. ### Proof: rref[A|AB]=[In|B] regarding determinants

The exercise wants us to show the following equality, by thinking in terms of block matrices. We`re supposed to used the fact that [B; In] is in the kernel of [In; M] rref[A AB] = [I M] and we must show the equality M=B. I am pretty clueless on how to approach this. A link to the proof or...