(a) Solve the following system of linear equations 3x2 + 2x3 +4x3 4 X4 0 + 6x₂ + X3 + X4 = 9 and write down the particular solution that satisfies x₂ = 0. 1 (b) Write down the inverse of the matrix A = (2² -5 solution X of the matrix equation X1 2x1 and hence find the unique AX = AT (c) Let u = (-1,1, -3), v = (3,2,-5) and w = (1, a, b) be vectors in R³ which satisfy u.w=v.w = 0. /...) (i) Determine a and b. (You may find part (b) helpful.) (ii) Verify that w = u x v. Write down ||w||.
(a) Solve the following system of linear equations 3x2 + 2x3 +4x3 4 X4 0 + 6x₂ + X3 + X4 = 9 and write down the particular solution that satisfies x₂ = 0. 1 (b) Write down the inverse of the matrix A = (2² -5 solution X of the matrix equation X1 2x1 and hence find the unique AX = AT (c) Let u = (-1,1, -3), v = (3,2,-5) and w = (1, a, b) be vectors in R³ which satisfy u.w=v.w = 0. /...) (i) Determine a and b. (You may find part (b) helpful.) (ii) Verify that w = u x v. Write down ||w||.
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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PLEASE ANSWER ALL PARTS OF QUESTION CLEARLY
Transcribed Image Text:(a) Solve the following system of linear equations
3x2 + 2x3
+ 4x3
X4 =
+ 6x2 + X3 + X4 =
X1
2x1
=
(b) Write down the inverse of the matrix A =
solution X of the matrix equation
4
0
9
and write down the particular solution that satisfies x₂ = 0.
1 -3
2 -5
and hence find the unique
AX = AT
(c) Let u = (–1,1,–3), v = (3,2,-5) and w = (1, a, b) be vectors in R³ which satisfy
u.w= v.w = 0.
(i) Determine a and b. (You may find part (b) helpful.)
(ii) Verify that w = u x v. Write down ||w||.
(iii) Hencre, or otherwise, calculate sin there is the angle between u and v.
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