Reduce the following matrices to row echelon form and row reduced echelon forms: [1 (i) 2 -1 -1 7 2 (ii) 2 1 1 7 1 -5 3 -3 3 2 3 2 0 Find also the ranks of these matrices.
Reduce the following matrices to row echelon form and row reduced echelon forms: [1 (i) 2 -1 -1 7 2 (ii) 2 1 1 7 1 -5 3 -3 3 2 3 2 0 Find also the ranks of these matrices.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Q1
Reduce the following matrices to row echelon form and row reduced
echelon forms:
[1
(i) 2
-1
-1
7
1
7
(ii) 2
1
-5
3
3 3
2
1
3
2
Find also the ranks of these matrices.
Q2
(i) Determine the currents for the electrical network shown in the following
figure, using Gauss elimination:
20 0
10v
20v
402
(ii) Find the volume of traffic along the arrows, using Gauss elimination:
18P
200
100
165
200
Q3
What situation arises in accordance with the Fundamental Theorem of
linear algebra for the systems given below:
x +y +z =p
(i) x +2y – z =4
Зх — у +2г %3-1
px +y +z =1
(ii) x +2y – z =4
Зрх + 3у +3z %3—1
x +y +z =p
(iї) — 2х — у —г %3D- 4
Зх + 3у +32 3 Зр
Transcribed Image Text:Q4(a)
Find a family of the matrices that is similar to the matrix
Q =
(b)
Find eigenvalues and eigenvectors of the following matrix:
[1 0 0
1
1
0 1
Determine (i) Eigenspace of each eigenvalue and basis of this
eigenspace (ii) Eigenbasis of the matrix
(c)
Is the matrix in part(b) is defective?
Q5(a)
Find the eigenbasis of the matrix and diagonalize it (if possible):
[4
A =\p
10 1
1
6
Use this diagonalization to find A' and A'.
(b)
For the matrix in part (i), find A² and A¯' using Cayley-Hamilton
theorem.
Q6 (a)
Sketch the vector and scalar fields. Describe the nature of vector fields.
Find also Curl and divergence in parts (i)-(iii). In parts (iv) and (v), find a
unit normal to the given surface at a point of your choice.
(i) F=x i-yj (ii) G=x i-y j
(iii) H=cos(x +y)i+sin(x –y)j,
(iv) f 3 4x — Зу + pz for -p<х,y <p.
(v) g = px² +5y² for -p<2x,2y <p.
http://user.mendelu.cz/marik/EquationExplorer/vectorfield.html
https://www.monroecc.edu/faculty/paulseeburger/calcnsf/CalcPlot3D/
Find the parametric form of (i) the circle x?+y? =p² (ii) the ellipse
(b)
2
=1 (ii) the straight line joining the points 1,2,4 and 2,p,7.
25
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