In exercise 1-4, W is a subspace of the vector space V of all ( 2 × 2 ) matrices. A matrix A in W is written as A = [ a b c d ] . In each case exhibit a basis for W . W = { A : b = a − c , d = 2 a + c }
In exercise 1-4, W is a subspace of the vector space V of all ( 2 × 2 ) matrices. A matrix A in W is written as A = [ a b c d ] . In each case exhibit a basis for W . W = { A : b = a − c , d = 2 a + c }
Solution Summary: The author explains the basis of subspace W: leftA:b=a-c,d=2a+cright.
In exercise 1-4,
W
is a subspace of the vector space
V
of all
(
2
×
2
)
matrices. A matrix A in
W
is written as
A
=
[
a
b
c
d
]
.
In each case exhibit a basis for
W
.
W
=
{
A
:
b
=
a
−
c
,
d
=
2
a
+
c
}
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.
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