Matrix algebra Definition and 66 Threads

Find X if X' * X = (50, 300) (300, 1000) Then find Y if Y * X = (300, 2000) Problem is that when I try to solve for X (or X') first, I get three equations with four unknowns (a11, a12, a21, a22). Any help?

Homework Statement You have 3 Vectors say v1,v2,v3 in R^4 meaning they each have 4 components. How do you determine if they are linearly dependent or independent? And usually how do you denote 4 components? I know everyone knows how to denote three components which is just x,y,z but idk what...

Homework Statement A range of metallic alloys are tested for electrical conductivity and give the following results for identically sized samples. 25% copper with 75% tin gave a reading of 0.0071 Ohms 65% copper with 35% cadmium gave a reading of 0.0049 Ohms 40% copper with 40% tin...

Suppose A^n=0 for some n>1. Find an inverse for I-A. I don't understand how to do this. It isn't homework, but I'm just studying.

Homework Statement If A is an nxn matrix such that A^3 = 0 (the zero matrix) then (I-A)^-1 = ...? A. not invertible B. I+A^2 C. I-A D. I+A E. I+A+A^2 Homework Equations The Attempt at a Solution I just don't know how to work out what the inverse of (I-A) is if I know A^3... how is this...

Homework Statement Find a vector w in R3 such that w is not a linear combination of v1 and v2 Homework Equations v1 = [1;2;-1] v2=[2;-1;-2] The Attempt at a Solution my question is : does w need to be in the span of v1 and v2?? Could i just choose [1; 1; 1] as my w vector??

1. Show that if a square matrix A satisfies A2 - 3A + I = 0, then A-1 = 3I - A 2. A-1A = I and A-1A = I and more that I can't think of 3. 3A = A2 + I A = (A2 + I)/3 ? This question is weird :o Anyone know how to do it?

Well I'm going to be taking Matrix Algebra next semester, and I have no clue what it's for. Wikipedia wasn't too enlightening. What is the purpose of matrix algebra, and what is is commonly used for?

Homework Statement Let a_1,...,a_n be Real. Then define a 2n x 2n matrix A as follows. The following are the first 4 and the last 2 columns; note that the (2k) column equals (a_k)(derivative of the (2k-1) column A[,1] = a_1^(2n),a_1^(2n-1),a_1^(2n-2),...,a_1^(2), a_1 A[,2] =...

Homework Statement Is the following true for matrices? Hypotesis: AB = AC A != 0(zero matrix) Thesis: B=C The Attempt at a Solution AB = AC AB - AC = 0(zero matrix) AB - AC = A(B-C) // using the following property: A(B+C) = AB + AC iff A is mn matrix and BC are np matrices...

Hi, We recently started analyzing linear machines using matrix algebra. Unfortunately, I haven't had much exposure to operating in finite fields aside from the extreme basics (i.e. the definitions of GF(P)). I can get matrix multiplication/addition, etc. just fine, but it's when finding the...

Homework Statement On page 44 of Ryder's QFT, near the bottom of the page, it says: Homework Equations Equation (2.94) is (\gamma^{\mu}p_{\mu} - m)\psi(p) = 0 The Attempt at a Solution Writing out all four components, and then taking the determinant and setting to zero, I get: m^4 - (E^2 -...

Homework Statement This is from Ryder's QFT book, second ed. page 37. At the bottom of the page it says that the commutation relations (eqn 2.68?) are satisfied by: K = \pm i\frac{\sigma}{2} However, I do not find this to be so. What am I missing? Homework Equations Here is one of the...

A=(5, 4) I (1, 0) (4,6) (0,1) Those are matrix by the way. How do I show A^2=11A-18I? I know I'm overlooking something, but i don't know what. Any tips would be helpful

Hi. Marix A= |1 1 0 | |0 2 0 | |2 1-1 | Has three eigenvectors [1,1,1]^T, [1,0,1]^T and [0,0,1]^T, By using this knowledge solve A^11. Ok, solving A^11 is rather easy with any decent calculator, or even with pen , paper and some time, but how on Earth I'm supposed to benefit...

Can someone explain to me how to use matrix algebra, to form a chemical equation?