Set A = floor ( 10 * rand ( 6 ) ) . By construction, the matrix A will have integer entries. Let us change the sixth column of A so as to make the matrix singular. Set B = A ' , A ( : , 6 ) = − sum ( B ( 1 : 5 , : ) ) r (a) Set x = ones ( 6 , 1 ) and use MATLAB to compute A x . Why do we know that A must be singular? Explain. Check that A is singular by computing its reduced row echelon form. (b) Set B = x * [ 1 : 6 ] The product A B should equal the zero matrix. Why? Explain. Verify that this is so by computing A B with the MATLAB operation *. (c) Set C = floor ( 10 * rand ( 6 ) ) and D = B + C Although C ≠ D , the products A C and A D should be equal. Why? Explain. Compute A * C and A * D , and verify that they are indeed equal.
Set A = floor ( 10 * rand ( 6 ) ) . By construction, the matrix A will have integer entries. Let us change the sixth column of A so as to make the matrix singular. Set B = A ' , A ( : , 6 ) = − sum ( B ( 1 : 5 , : ) ) r (a) Set x = ones ( 6 , 1 ) and use MATLAB to compute A x . Why do we know that A must be singular? Explain. Check that A is singular by computing its reduced row echelon form. (b) Set B = x * [ 1 : 6 ] The product A B should equal the zero matrix. Why? Explain. Verify that this is so by computing A B with the MATLAB operation *. (c) Set C = floor ( 10 * rand ( 6 ) ) and D = B + C Although C ≠ D , the products A C and A D should be equal. Why? Explain. Compute A * C and A * D , and verify that they are indeed equal.
Solution Summary: The author calculates the multiplication of the matrices and row reduced echelon form using a given relation.
Set
A
=
floor
(
10
*
rand
(
6
)
)
. By construction, the matrix A will have integer entries. Let us change the sixth column of A so as to make the matrix singular. Set
B
=
A
'
,
A
(
:
,
6
)
=
−
sum
(
B
(
1
:
5
,
:
)
)
r
(a) Set
x
=
ones
(
6
,
1
)
and use MATLAB to compute
A
x
. Why do we know that A must be singular? Explain. Check that A is singular by computing its reduced row echelon form. (b) Set
B
=
x
*
[
1
:
6
]
The product
A
B
should equal the zero matrix. Why? Explain. Verify that this is so by computing
A
B
with the MATLAB operation *. (c) Set
C
=
floor
(
10
*
rand
(
6
)
)
and
D
=
B
+
C
Although
C
≠
D
, the products
A
C
and
A
D
should be equal. Why? Explain. Compute
A
*
C
and
A
*
D
, and verify that they are indeed equal.
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