1. Suppose A = (3,3,6) is a linear system of three equations in three variables whose full solution set is = (-3 2s + t, s, t), where s, t e R. Find, with explanation, the coefficient matrix A.
1. Suppose A = (3,3,6) is a linear system of three equations in three variables whose full solution set is = (-3 2s + t, s, t), where s, t e R. Find, with explanation, the coefficient matrix A.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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MATH 211 Homework #2
(due Thursday, 15 October 2020 at 7pm)
1. Suppose A = (3, 3, 6) is a linear system of three equations in three variables whose
full solution set is = (-3 2s + t, s, t), where s, t E R. Find, with explanation, the
coefficient matrix A.
2. Let I be the 3 x 3 identity matrix and J be the 3 x 3 matrix with every entry equal to
1. Let S be the set of all linear combinations of I and J.
(a) Show that S is the set of all 3 x 3 matrices which are constant on the diagonal
and constant off the diagonal.
(b) Prove that the product of any two matrices in S is also in S.
1 1
3. Let F
1
0.
a) Compute F², F³, Fª and F5.
1
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