Euclidean Linear Dependence

Is K={f_1(x)=1, f_2(x)=sin x, f_3(x)=cos x }cC[0,1] linearly independent or linearly dependent? Justify your answer.

Euclidean Linear Dependence

1. Is H= the column vectors of the matrix M= [1 0 2 0] cR^4 linearly independent or [4 0 3 0] linearly dependent? [5 0 -1 0] Justify your answer. [-2 -3 1 1] Help: [1 0 2 0] [4 0 3 0] [5 0 -1 0] is a 4x4 matrix [-2 -3 1 1]

Linear Dependence

Write a proof for the following result: Any set consisting of two non-zero vectors is linearly independent if, and only if, one vector is not a scalar multiple of the other. Show work.

Systems of Linear Equations : 3 Unknowns (Echelon Method)

The problem is to find all the possible solutions to the following: Eq 1: x + y = 2 Eq 2: y + z = 3 Eq 3: x + 2y + z = 5 I set up my matricies in the following: 1 1 0 2 0 1 1 3 1 2 1 5 operation 1: (-1*row 1 +row 3) 1 1 0 2 0 1 1 3 0 1 1 3 operation 2: (-1*row 2 +row 3) 1 1 0 2 0 1 1 3 0 0 0 0 operation 3: (-1*row 2 +row 1) 1 0 -1 -1 0 1 1 3 0 0 0 0 I am taking a optimization class, but I have never had linear algebra. From the review problems in the book, I have got this far, but I don't know what else I could do now operational wise that would make sense, and I don't know what this means to the solution. Can you help explain it ... click for more

Matrix Proof: Determinants

Please see the attached file for the full problem description: 1. Show that if   0, then A^-1=1/ [ d -b ] [ -c a ] . Help: : is the determinant A [ d -b] [ -c a ] : is a 2 x 2 matrices