Question

Given the following vector X, find a non-zero square matrix A
such that AX=0:

You can resize a matrix (when appropriate) by clicking and dragging
the bottom-right corner of the matrix.

x = [-1]

[10]

[-4]

This is a 3x1 matrix.

Answer #1

Consider the following system of linear equations:
2x1−2x2+4x3
=
−10
x1+x2−2x3
=
5
−2x1+x3
=
−2
Let A be the coefficient matrix and X the solution matrix to the
system. Solve the system by first computing A−1 and then
using it to find X.
You can resize a matrix (when appropriate) by clicking and dragging
the bottom-right corner of the matrix.

Solve the following system of linear equations: 3x2−9x3 = −3
x1−2x2+x3 = 2 x2−3x3 = 0 If the system has no solution, demonstrate
this by giving a row-echelon form of the augmented matrix for the
system. If the system has infinitely many solutions, your answer
may use expressions involving the parameters r, s, and t. You can
resize a matrix (when appropriate) by clicking and dragging the
bottom-right corner of the matrix.

Find the fundamental matrix solution for the system x′ = Ax
where matrix A is given. If an initial condition is provided, find
the solution of the initial value problem using the principal
matrix.
A= [ 4 -13 ; 2 -6 ]. , x(o) = [ 2 ; 0 ]

4. Suppose that we have a linear system given in matrix form as
Ax = b, where A is an m×n matrix, b is an m×1 column vector, and x
is an n×1 column vector. Suppose also that the n × 1 vector u is a
solution to this linear system. Answer parts a. and b. below.
a. Suppose that the n × 1 vector h is a solution to the
homogeneous linear system Ax=0.
Showthenthatthevectory=u+hisasolutiontoAx=b.
b. Now, suppose that...

Given a matrix system AX = B as below, where A is a 4 x 4
matrix as given below
A:
2
1
0 0
1
2
1 0
0
2
4 1
0
0
1 3
B:
0
-1
3
-1
Solve for all 4 X values using TDMA
algorithm
First identify the a, d, c and b values for each row, and then
find P’s and Q’s and finally determine X’s.

a) Find the steady-state vector for the transition matrix.
.8
1
.2
0
x= ______
__________
b) Find the steady-state vector for the transition matrix.
1
7
4
7
6
7
3
7
These are fractions^
x= _____
________

A) Find the inverse of the following square matrix.
I 5 0 I
I 0 10 I
(b) Find the inverse of the following square matrix.
I 4 9 I
I 2 5 I
c) Find the determinant of the following square matrix.
I 5 0 0 I
I 0 10 0 I
I 0 0 4 I
(d) Is the square matrix in (c) invertible? Why or why not?

(a) Find the inverse of the following square
matrix.
I 5 0 I
I 0 10 I
(b) Find the inverse of the following square
matrix.
I 4 9 I
I 2 5 I
(c) Find the determinant of the following square
matrix.
I 5 0 0 I
I 0 10 0 I
I 0 0 4 I
(d) Is the square matrix in (c) invertible? Why or why
not?

You are given a transition matrix P. Find the
steady-state distribution vector. HINT [See Example 4.]
P =
3/4
1/4
8/9
1/9
You are given a transition matrix P. Find the
steady-state distribution vector. HINT [See Example 4.]
P =
4/5
1/5
0
5/6
1/6
0
5/9
0
4/9

*** Write a function called reverse_diag that creates a square
matrix whose elements are 0 except for 1s on the reverse diagonal
from top right to bottom left. The reverse diagonal of an n-by-n
matrix consists of the elements at the following indexes: (1, n),
(2, n-1), (3, n-2), … (n, 1). The function takes one positive
integer input argument named n, which is the size of the matrix,
and returns the matrix itself as an output argument. Note that...

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