help with linear algebra
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m221_19S_Q-8.pdf
M 221 Quiz 8 — Name: Include work for partial credit, but please put final answer in provided box. Upload completed document to Gradescope by Friday, 3/29, 1:10pm (or bring to class).
1. Consider A = [ a1 a2 a3
] =
1 1 11 −1 0
2 0 4
.
(a) (3 points) From the vectors a1, a2, a3 find orthonormal vectors q1, q2, q3 by Gram-Schmidt. Write them in terms of the matrix Q =
[ q1 q2 q3
] .
Q =
(b) (2 points) Compute the upper triangular matrix R such that A = QR, with Q = [ q1 q2 q3
] . Hint:
Either use the approach from class or note A = QR, thus QT A = QT QR. Now Q has orthonormal columns, therefore QT Q =? and QT A =?
R =
