Linear Algebra Quiz
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INNER PRODUCT SPACES & ORTHOGONALITY
Question 1
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Find the least-squares solution
x
^
\hat{x}
x
^
for the system
A
x
⃗
=
b
⃗
A\vec{x} = \vec{b}
A
x
=
b
where
A
=
(
1
0
1
1
1
2
)
A = \begin{pmatrix} 1 & 0 \\ 1 & 1 \\ 1 & 2 \end{pmatrix}
A
=
1
1
1
0
1
2
and
b
⃗
=
(
6
0
0
)
\vec{b} = \begin{pmatrix} 6 \\ 0 \\ 0 \end{pmatrix}
b
=
6
0
0
.
A
(
6
−
6
)
\begin{pmatrix} 6 \\ -6 \end{pmatrix}
(
6
−
6
)
B
(
−
1
3
)
\begin{pmatrix} -1 \\ 3 \end{pmatrix}
(
−
1
3
)
C
(
30
−
18
)
\begin{pmatrix} 30 \\ -18 \end{pmatrix}
(
30
−
18
)
D
(
5
−
3
)
\begin{pmatrix} 5 \\ -3 \end{pmatrix}
(
5
−
3
)
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