LINEAR ALGEBRA MATLAB
I will greatly appreciate it if you could provide me the "MATLAB CODES". Please do not try to solve it by handwriting. all i need is the matlab codes :)
I'll make sure to give you thumbs up within 6 hrs! thanks so much for your time and help!
PLEASE ANSWER PART e,f,g,h ONLY!! for your information, part a,b,c,d was done and can be found here:https://www.chegg.com/homework-help/questions-and-answers/hello-matlab-hw-linear-algebra-course-plase-provide-matlab-codes-thank-much-also-question--q25373001
3. Let W be the subspace of R5 given by 15 13 W = Span 13 24 16 (a) Enter the four vectors into MATLAB as vi, v2, v3 and v4 respectively (b) Let A -[vl v2 v3 v4]. Compute the rank of this matrix. Explain briefly in a comment why this shows that this set of four vectors is a basis for W (c) We shall apply the Gram-Schmidt Process to produce an orthogonal basis {wi, w2, w3, wA) for W. To begin, let w1 = v1 and w2 -v2- (dot (wi,v2) /dot (wi,wi))*wi (d) Continue the Gram-Schmidt Process and compute w3 and w4 (e) Rescale each vector of the orthogonal basis [wi, w2, w3, wa to produce an orthonormal basis ^u1, u2, uz, u4) for W. (Recall there is a command in MATLAB to compute the norm of a vector.) (f) Enter the vectors u1, u2, U3, u4 into the columns of a matrix Q. Verify that the columns of Q are (g) Compute R- Q7 A. Verify that R is upper triangular with positive diagonal entries and that (h) MATLAB can compute a QR factorization in a single command. Enter [Q1, R1] - r(A,0) orthonormal with a single matrix multiplication. A = QR. Notice that there is a small discrepancy between your Q, R and the Q1, R1 produced by MATLAB This is because QR factorizations are not unique. They are only unique if we insist that the diagonal entries of R are all postive. Nonetheless, the columns of Q1 still form an orthonormal basis for W 3. Let W be the subspace of R5 given by 15 13 W = Span 13 24 16 (a) Enter the four vectors into MATLAB as vi, v2, v3 and v4 respectively (b) Let A -[vl v2 v3 v4]. Compute the rank of this matrix. Explain briefly in a comment why this shows that this set of four vectors is a basis for W (c) We shall apply the Gram-Schmidt Process to produce an orthogonal basis {wi, w2, w3, wA) for W. To begin, let w1 = v1 and w2 -v2- (dot (wi,v2) /dot (wi,wi))*wi (d) Continue the Gram-Schmidt Process and compute w3 and w4 (e) Rescale each vector of the orthogonal basis [wi, w2, w3, wa to produce an orthonormal basis ^u1, u2, uz, u4) for W. (Recall there is a command in MATLAB to compute the norm of a vector.) (f) Enter the vectors u1, u2, U3, u4 into the columns of a matrix Q. Verify that the columns of Q are (g) Compute R- Q7 A. Verify that R is upper triangular with positive diagonal entries and that (h) MATLAB can compute a QR factorization in a single command. Enter [Q1, R1] - r(A,0) orthonormal with a single matrix multiplication. A = QR. Notice that there is a small discrepancy between your Q, R and the Q1, R1 produced by MATLAB This is because QR factorizations are not unique. They are only unique if we insist that the diagonal entries of R are all postive. Nonetheless, the columns of Q1 still form an orthonormal basis for W
