In the text we defined a matrix A to be symmetric if A T = A. Analogously, a matrix A is said to be skew-symmetric if A T = −A. Exercises 41–45 are concerned with matrices of this type. Find all values of a , b , c , and d for which A is skew-symmetric. A = [ 0 2 a − 3 b + c 3 a − 5 b + 5 c − 2 0 5 a − 8 b + 6 c − 3 − 5 d ]
In the text we defined a matrix A to be symmetric if A T = A. Analogously, a matrix A is said to be skew-symmetric if A T = −A. Exercises 41–45 are concerned with matrices of this type. Find all values of a , b , c , and d for which A is skew-symmetric. A = [ 0 2 a − 3 b + c 3 a − 5 b + 5 c − 2 0 5 a − 8 b + 6 c − 3 − 5 d ]
In the text we defined a matrix A to be symmetric if AT = A. Analogously, a matrix A is said to be skew-symmetric if AT = −A. Exercises 41–45 are concerned with matrices of this type.
Find all values of a, b, c, and d for which A is skew-symmetric.
A
=
[
0
2
a
−
3
b
+
c
3
a
−
5
b
+
5
c
−
2
0
5
a
−
8
b
+
6
c
−
3
−
5
d
]
Unless otherwise specified, assume that all matrices in these exercises are nxn. Determine which of the matrices in Exercises 1–10 are invertible. Use as few calculations as possible. Justify your answers
In Exercises 11–16, compute the adjugate of the given matrix, and
then use Theorem 8 to give the inverse of the matrix.
Find the inverses of the matrices in Exercises 1–4.
College Algebra with Modeling & Visualization (5th Edition)
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