1. The problem statement, all variables and given/known data Find a singular value decomposition of A. A^T= [7 0 5 1 0 5] 2. Relevant equations A = U[tex]\Sigma[/tex]V^T 3. The attempt at a solution I started by doing A^T*A = [ 74 32 32 26] Then i went and found the two eigen values lambda1= 90 and lambda2= 10 and the eigenvectors v1 = [2 1]^T and v2 = [-1 2]^T So, I have V and V^T From this the singular values are sigma_1 = sqrt(90) and sigma_2 = sqrt(10) So, [tex]\Sigma[/tex] in this decomposition would be [ sqrt(90) 0 0 sqrt(10) 0 0] Now to figure out U. u_1 = 1/sigma_1 AV1 which is = [ 15/sqrt(90) 0 15/sqrt(90)]^T and I did the same thing for u_2 to get [-5/sqrt(10) 0 5/sqrt(10)] Now, this is where I get stuck. I know I need U to be 3x3 for the matrix multiplication to work out. My book says to find an orthogonal vector and use the gramschmidt method to get u_3. Do I need it to be orthogonal to u_1 or u_2? or both? Also I can't figure out the gramschmidt. If someone could please clarify this for me that would really help. I'm so close (if what I already did is correct) but I can't figure it out.