Question

Using elementary transformations, determine matrices B and C so that BAC=I for the matrix A. Use B and C to compute the inverse of A; that is, take the inverse of both sides of the equation BAC=I and then solve for A inverse.

I need to find Matrix B, Matrix C, and Inverse of matrix A

A=

1 2 1 1

0 1 2 0

1 2 2 1

0 -1 1 2

Answer #1

Solving Systems of Linear Equations Using Linear
Transformations
In problems 2 and 5 find a basis for the solution set of the
homogeneous linear systems.
2. ?1 + ?2 + ?3 = 0
?1 − ?2 − ?3 = 0
5. ?1 + 2?2 − 2?3 + ?4 = 0
?1 − 2?2 + 2?3 + ?4 = 0.
So I'm in a Linear Algebra class at the moment, and the
professor wants us to work through our homework using...

a).For the reduction of matrix determine the elementary matrices
corresponding to each operation. M= 1 0 2 1 5
1 1 5 2 7
1 2 8 4 12 b). Calculate the product P of these elementary
matrices and verify that PM is the end result.

True or False (Please explain)
1. If E and F are elementary matrices then C = E*F is
nonsingular.
2. If A is a 3x3 matrix and
a1+2a2-a3=0 then A must be
singular.
3. If A is a 3x3 matrix and
3a1+a2+4a3=b is consistent.

use matrix manipulation to solve for a, b, and c. Set up a
matrix equation for AX=B based on the system of equations below,
where X is a matrix of the variables a, b and c. Then, use
Gauss-Jordan elimination to find the inverse of A. Finally, use
your results to write the equation of the parabola. Show your work
and final equation in the space provided. 9a+3b+c=8 ,
25a+5b+c=20/3, 36a+6b+c=5

write the following matrices as a product of elementary
matrices:
a)
1 2
4 9
b)
1 -2 -1
-1 5 6
5 -4 5
c)
1 0 -2
-3 1 4
2 -3 4

1). Show that if AB = I (where I is the identity matrix) then
A is non-singular and B is non-singular (both A and B are nxn
matrices)
2). Given that det(A) = 3 and det(B) = 2, Evaluate (numerical
answer) each of the following or state that it’s not possible to
determine the value.
a) det(A^2)
b) det(A’) (transpose determinant)
c) det(A+B)
d) det(A^-1) (inverse determinant)

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?

A=
2
-3
1
2
0
-1
1
4
5
Find the inverse of A using the method: [A | I ] → [ I | A-1 ].
Set up and then use a calculator (recommended). Express the
elements of A-1 as fractions if they are not already integers. (Use
Math -> Frac if needed.) (8 points)
Begin the LU factorization of A by determining a first
elementary matrix E1 and its inverse E1-1. Identify the associated
row operation. (That...

I) Use MATLAB to compute the determinants of the following two
matrices. (Use format rat)
P
Q
5
0
0
0
-1
-1
1
1
13
2
0
0
2
0
1
3
-6
4
-1
0
2
-1
1
2
10
0
3
-2
1
0
3
3
II) The determinant of P could be computed without MATLAB. What
general fact could have been used to do this?
III) Use MATLAB to compute the matrix R= PQ and also...

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