 # Engineering analysis discussion questions Anonymous
timer Asked: Feb 19th, 2019
account_balance_wallet \$5

### Question Description

When you give solutions, make sure you give step-by-step procedures and explanations to show your reasoning and justifications.

Attachment preview

1. (Points 10) Matrix A is singular: True or False? justify.

2. (Points 20) Find A – B, B + A + +,

3. (Points 20) Is it true: AB = BA? justify.

4. (Points 30) -.X = d, find X using Gauss-Jordan elimination method.

• Step 1: Write down the system of linear equations

• Step 2: Construct the augmented coefficient matrix.

• Step 3: Apply Gauss-Jordan elimination.

• Step 4: Reduced to row-echelon form.

5. (Points 20) Find the inverse of matrix B using Gauss-Jordan elimination method.

HW 2 EGN 3420 Engineering Analysis Deadline: 02/22/2019 (Friday) 11:59 PM &' 1 0 2 2 0 1 1 & A = !1 2 0%, B = !2 1 0%, X = ! ( %, d = !−1% &) 0 1 2 0 2 1 0 1. (Points 10) Matrix A is singular: True or False? justify. 2. (Points 20) Find A – B, B + A + +, 3. (Points 20) Is it true: AB = BA? justify. 4. (Points 30) -. X = d, find X using Gauss-Jordan elimination method. • Step 1: Write down the system of linear equations • Step 2: Construct the augmented coefficient matrix. • Step 3: Apply Gauss-Jordan elimination. • Step 4: Reduced to row-echelon form. 5. (Points 20) Find the inverse of matrix B using Gauss-Jordan elimination method.

seniorlecturerken
School: Purdue University   Hey there. I've managed to solve the problems. Kindly go through them and let me know if any of the solutions isn't clear.

Concepts:
1.
2.
3.
4.
5.
6.

Identity matrices
Gauss Jordan elimination method
Matrix transposition
Inverse of a matrix
Matrix multiplication

Question 1
Solution
A matrix is singular if and only if the determinant is zero.
𝑎11 𝑎12
For a matrix A = [𝑎21 𝑎22
𝑎31 𝑎32

𝑎13
𝑎23]
𝑎33

The determinant can be found by rewriting the matrix in the below form where column 1 and 2
are repeated;
𝑎11 𝑎12
[𝑎21 𝑎22
𝑎31 𝑎32

𝑎13 𝑎11
𝑎23 𝑎21
𝑎33 𝑎31

𝑎12
𝑎22]
𝑎32

The determinant is then obtained by subtracting the lagging product sum from the leading
product sum as shown below;
Determinant = (a11*a22*a33 + a12*a23*a31 + a13*a21*a32) –
(a31*a22*a13 + a32*a23*a11 + a33*a21*a12)
1 0 2
For the matrix A = [1 2 0]
0 1 2
The matrix above can be rewritten as;
1 0 2 1 0
[1 2 0 1 2 ]
0 1 2 0 1
The determinant is therefore given by;
Det = (1*2*2 + 0*0*0 + 2*1*1) – (0*2*2 + 1*0*1 + 2*1*0)
Det = (4 + 0 + 2 ) – (0 + 0 + 0)
Det = 6

Since the determinant of matrix A is not zero. The matrix is therefore not singular i.e the
statement is false as justified above

Question Two
Finding A – B

I.

For two matrices A and B their difference can be expressed as below;
𝑎11 𝑎12
[𝑎21 𝑎22
𝑎31 𝑎32

𝑎13
𝑏11
𝑎23] - [𝑏21
𝑎33
𝑏31

𝑏12
𝑏22
𝑏32

1
For A = [1
0

0 2
2 0
2 0] and B = [2 1
1 2
0 2

1
A – B = [1
0

0 2
2
2 0] - [2
1 2
0

II.

𝑏13
𝑎11 − 𝑏11
𝑏23] = [𝑎21 − 𝑏21
𝑏33
𝑎31 − 𝑏31

𝑎12 − 𝑏12
𝑎22 − 𝑏22
𝑎32 − 𝑏32

𝑎13 − 𝑏13
𝑎23 − 𝑏23]
𝑎33 − 𝑏33

1
0]
1

0 1
−1 0 1
1 0] = [−1 1 1]
2 1
0 −1 1

Finding B + A + I3

Note that I3 is a 3x3 identity matrix which can be expressed as;
1
I3 = [0
0

0 0
1 0]
0 1

Therefore B + A + I3 will be given by;
2 0 1
1 0 2
1 0
B + A + I3 = [2 1 0] + [1 2 0] + [0 1
0 2 1
0 1 2
0 0
4 0 3
B + A + I3 = [3 4 0]
0 3 4

2+1+1 0+0+0
0
0] = [2 + 1 + 0 1 + 2 + 1
0+0+0 2+1+0
1

1+2+0
0 + 0 + 0]
1+2+1

Question Three
Consider two matrices;
𝑎11 𝑎12 𝑎13
𝑏11
A = [𝑎21 𝑎22 𝑎23] 𝑩 = [𝑏21
𝑎31 𝑎32 𝑎33
𝑏31

AB =
𝑎11 ∗ 𝑏11 + 𝑎12 ∗ 𝑏21 + 𝑎13 ∗ 𝑏31
[𝑎21 ∗ 𝑏11 + 𝑎22 ∗ 𝑏21 + 𝑎23 ∗ 𝑏31
𝑎31 ∗ 𝑏11 + 𝑎32 ∗ 𝑏21 + 𝑎33 ∗ 𝑏3...

flag Report DMCA  Review Anonymous
Excellent job Brown University

1271 Tutors California Institute of Technology

2131 Tutors Carnegie Mellon University

982 Tutors Columbia University

1256 Tutors Dartmouth University

2113 Tutors Emory University

2279 Tutors Harvard University

599 Tutors Massachusetts Institute of Technology

2319 Tutors New York University

1645 Tutors Notre Dam University

1911 Tutors Oklahoma University

2122 Tutors Pennsylvania State University

932 Tutors Princeton University

1211 Tutors Stanford University

983 Tutors University of California

1282 Tutors Oxford University

123 Tutors Yale University

2325 Tutors