In Exercises 9–10 , use matrices A and B from Exercises 7–8. a. Express each column vector of AB as a linear combination of the column vectors of A . b. Express each column vector of BA as a linear combination of the column vectors of B . In Exercises 7–8 , use the following matrices and either the row method or the column method, as appropriate, to find the indicated row or column. A = [ 3 − 2 7 6 5 4 0 4 9 ] and B = [ 6 − 2 4 0 1 3 7 7 5 ]
In Exercises 9–10 , use matrices A and B from Exercises 7–8. a. Express each column vector of AB as a linear combination of the column vectors of A . b. Express each column vector of BA as a linear combination of the column vectors of B . In Exercises 7–8 , use the following matrices and either the row method or the column method, as appropriate, to find the indicated row or column. A = [ 3 − 2 7 6 5 4 0 4 9 ] and B = [ 6 − 2 4 0 1 3 7 7 5 ]
In Exercises 9–10, use matrices A and B from Exercises 7–8.
a. Express each column vector of AB as a linear combination of the column vectors of A.
b. Express each column vector of BA as a linear combination of the column vectors of B.
In Exercises 7–8, use the following matrices and either the row method or the column method, as appropriate, to find the indicated row or column.
A
=
[
3
−
2
7
6
5
4
0
4
9
]
and
B
=
[
6
−
2
4
0
1
3
7
7
5
]
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Find the inverses of the matrices in Exercises 1–4.
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 5–8, use the definition of to write the matrix equation as a vector equation, or vice versa.
College Algebra with Modeling & Visualization (6th Edition)
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