Given vectors \mathbf{v} = ⎡⎣−4−38⎤⎦
v=
⎣
⎢
⎡
​

−4
−3
8
​

⎦
⎥
⎤
​
, \mathbf{b_1} =
⎡⎣123⎤⎦
b
1
​
=
⎣
⎢
⎡
​

1
2
3
​

⎦
⎥
⎤
​
, \mathbf{b_2} =
⎡⎣−210⎤⎦
b
2
​
=
⎣
⎢
⎡
​

−2
1
0
​

⎦
⎥
⎤
​
and \mathbf{b_3} =
⎡⎣−3−65⎤⎦
b
3
​
=
⎣
⎢
⎡
​

−3
−6
5
​

⎦
⎥
⎤
​
all written in the standard basis, what is \mathbf{v}v in the basis defined by \mathbf{b_1}b
1
​
, \mathbf{b_2}b
2
​
and \mathbf{b_3}b
3
​
? You are given that \mathbf{b_1}b
1
​
, \mathbf{b_2}b
2
​
and \mathbf{b_3}b
3
​
are all pairwise orthogonal to each other.