Additional Problems
1.(Matlab) Create a random matrix
A
using the command
A
= floor(10
*
rand(4
,
4))
.
(a) Swap the first and second row of
A
to get the matrix
B
using the commands:
B
=
A
;
B
([1
,
2]
,
:) =
B
([2
,
1]
,
:)
What relation between det(
A
) and det(
B
) from the properties of the determi
nant in Section 2.2. Check your answer by calculating det(
A
) and det(
B
) using
Matlab.
(b) Let
C
be the matrix obtained from
A
by multiplying the first row of
A
by
10 and adding to the second row of
A
using the commands:
C
=
A
;
C
(2
,
:) =
A
(2
,
:) + 10
*
A
(1
,
:)
What relation between det(
A
) and det(
C
) from the properties of the determi
nant in Section 2.2. Check your answer by calculating det(
A
) and det(
C
) using
Matlab.
(c) Let D be the matrix obtained from
A
by multiplying the first and the second
row of
A
by 2 and 3, respectively, using the commands:
D
=
A
;
D
(1
,
:) = 2
*
A
(1
,
:);
D
(2
,
:) = 3
*
A
(2
,
:)
What relation between det(
A
) and det(
D
) from the properties of the determi
nant in Section 2.2. Check your answer by calculating det(
A
) and det(
D
) using
Matlab.
2.(Matlab) Theorem 2.2.2 tells that the determinant of the matrix is zero if
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 Spring '08
 KIM
 Linear Algebra, Algebra, matlab, Addition, Invertible matrix, Det, A100

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