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Gaussian Elimination & Matrix Ops Homework for SURE 372 at Ferris State Univ., Assignments of Engineering

Ferris State University (FSU)Engineering

A homework assignment for the sure 372 adjustment computations course at ferris state university. The assignment involves solving systems of linear equations using gaussian elimination and gauss-jordan elimination, as well as performing matrix operations such as addition and multiplication. Students are expected to find echelon forms and reduced echelon forms of matrices, and perform vector multiplications.

Typology: Assignments

Pre 2010

Uploaded on 08/07/2009

koofers-user-lmq
koofers-user-lmq 🇺🇸

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bg1
1. Solve the following systems of equations using Gaussian elimination
a) 1262
42
21
21
=+
=+
xx
xx b)
12
4642
22
321
321
32
=++−
=−+
=−
xxx
xxx
xx
2. Solve the following linear equation using Gauss-Jordan elimination
11732
169432
4
431
4321
4321
=−+−
=+++
=+++
xxx
xxxx
xxxx
3. Solve the following problems by placing the linear equations into the augmented
matrix then to echelon form
a)
2
543
62
321
321
321
=++−
=−+
=++
xxx
xxx
xxx
b)
23
232
1
321
321
321
=+−
=++
=++
xxx
xxx
xxx
4. Solve the following systems of linear equations by transforming the augmented
matrix to reduced echelon form
a)
032
3434
2332
321
321
321
=++
=++−
−=−−
xxx
xxx
xxx
b)
146
432
532
21
31
321
=+
−=+−
=++
xx
xx
xxx
5. Given the following matrices, find
=31
12
A
−
=31
10
B
−
=11
32
C
a) A + B
b) A + C
c) B + 3C
d) a matrix D such that A + 2D = C
e) a matrix D such that 2A + 5B + D = 2B + 3A
SURVEYING ENGINEERING
FERRIS STATE UNIVERSITY
SURE 372 Adjustment Computations 1 Fall 2005/06
Homework #2
pf2

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Download Gaussian Elimination & Matrix Ops Homework for SURE 372 at Ferris State Univ. and more Assignments Engineering in PDF only on Docsity!

  1. Solve the following systems of equations using Gaussian elimination

a) 2 6 12

1 2

1 2

  • =

x x

x x b)

2 1

1 2 3

1 2 3

2 3

x x x

x x x

x x

  1. Solve the following linear equation using Gauss-Jordan elimination

1 3 4

1 2 3 4

1 2 3 4

x x x

x x x x

x x x x

  1. Solve the following problems by placing the linear equations into the augmented

matrix then to echelon form

a)

2

1 2 3

1 2 3

1 2 3

x x x

x x x

x x x

b)

3 2

1 2 3

1 2 3

1 2 3

x x x

x x x

x x x

  1. Solve the following systems of linear equations by transforming the augmented

matrix to reduced echelon form

a)

2 3 0

1 2 3

1 2 3

1 2 3

x x x

x x x

x x x

b)

6 14

1 2

1 3

1 2 3

x x

x x

x x x

  1. Given the following matrices, find

A 

B 

C

a) A + B

b) A + C

c) B + 3C d) a matrix D such that A + 2D = C

e) a matrix D such that 2A + 5B + D = 2B + 3A

SURVEYING ENGINEERING

FERRIS STATE UNIVERSITY

SURE 372 Adjustment Computations 1 Fall 2005/

Homework

  1. Using the following vectors and matrices given in the previous question, find

r (^)  

s (^)  

t (^)  

u

a) t + s

b) 2r + t

c) 2u + 3t

d) Bt e) (B + C)u

  1. Given the following matrices and vectors, compute

A 

B

C

D 

u v =[ 2 4 ]

a) AB and BA

b) Au and vA

c) DC

d) uv and vu

e) (AB)u and A(Bu) f) (BA)u and B(Au)