Recent content by LosTacos

(A - 13I)x = 0: {[10, 4, 12, 0],[4, 1, 3, 0],[12, 3, 17]} = {[1, 2/5, 6/5],[4, 1, 3, 0],[12, 3, 17, 0]} = {[1, 2/5, 6/5, 0], [0, -3/5, -9/5, 0],[0, -9/5, 13/5, 0]} = {[1, 2/5, 6/5, 0],[0, 1, 3, 0], [0, 0, 8, 0]}

Okay I understand. So my eigenvalues are 13 and -13. If I was asked to find the basis for both of these, how do I go about doing that. I tried to solve the equation [13I2 - A I 0] however if ran into a wall. I row reduced it to get the matrix = {[2, 2/5, 6/5], [0,1,3], [0,0,1]}. But I wasnt sure...

From the characteristic polynomial x3 + 13x2 + 2053, how do I get the correct eigenvalues?

Because the columns of A are linearly independent, each column will have a unique solutions such that there will exist an x such that L(x)=b which implies Ax=B

Actually I forgot to calculate teh determinants so I got: Pa(x) = (x-3)(x+12)(x+4) + 2197 = x3 + 13x2 + 2053

Homework Statement Find eigenvalue for matrix B= {[3,4,12],[4,-12,3],[12,3,-4]} Homework Equations The Attempt at a Solution I set up the charactersitic polynomial and got the equation: Pa(x) = (x-3)(x+12)(x+4) = x3 + 132 - 144 + 144 = x3 + 132 So I have 3 eigenvalues: 0...

thank you

so how do you go about showing it is surjective

Okay, so given those two solutions, do I row reduce it to determine teh basis?

Okay so the equation has the trivial solution. So that means that the only solution is the trivial one, which is represented by the columns themselves, therefore 1-1. And since C is linearly independent, no vector in the matrix can be expressed as a linear combination of otheres. Therefore, each...

Well to prove that each side is equal to one another, I have to prove that each is a subset of the other. In essence, prove it both ways. So when doing the dot product of [a1, a2, ..., an] ⋅ [c1, c2, ..., cn] are you saying that i need to create 9 different products for this example. And then bc...

I am confused as to what is correct for the reverse direction. From the definition of coordinatization, Let B = (b1, b2, ..., bk) be an ordered basis. Suppose v1= a1b1 + a2b2 + ... + anbn. Then, [v1]B, the coordinatization of v1 with respect to B is the n-vector [a1, a2, ..., an] So if this...

Homework Statement Given matrix A= {[39/25,48/25],[48/25,11/25]} find the basis for both eigenvalues. Homework Equations The Attempt at a Solution I row reduced the matrix and found both eigenvalues. I found λ = -1, and λ = 3. Then, I used diagonalization method [-1I2 - A 0]...

Homework Statement Let L:R->R be a linear operator with matrix C. Prove if the columns of C are linearly independent, then L is an isomorphism. Homework Equations The Attempt at a Solution Assume the columns of C are linearly independent. Then, the homogenous equation Cx=0 is...

I could of defined L(C)=B such that if i>k, then L(vi) = ker(L) = B = 0