Question 4
Let u and v be 3-dimensional vectors, where specifically
u =
⎡⎣4−4−3⎤⎦
u= ⎣
⎢
⎡
4
−4
−3
⎦
⎥
⎤
and
v =
⎡⎣424⎤⎦
v= ⎣
⎢
⎡
4
2
4
⎦
⎥
⎤
What is u^Tvu T
v?
(Hint: u^Tu T
is a
1x3 dimensional matrix, and v can also be seen as a 3x1
matrix. The answer you want can be obtained by taking
the matrix product of u^Tu T
and vv.) Do not add brackets to your answer.
Answers
Answer:
Given: u and v be 3-dimensional vectors.
To find: The value of u^T v
Solution:
Now we have given u and v be 3-dimensional vectors.
u = [ 3 4 3 ]
v = [ 3 1 5 ]
Now :
u^T = \begin{gathered}[\begin{array}{ccc}3\\4\\3\end{array}]\end{gathered}
[
3
4
3
]
So the order of u^T is 3 x 1 and v is 1 x 3
So the resultant matrix will be of order 3 x 3.
u^T v = \begin{gathered}[\begin{array}{ccc}3\\4\\3\end{array}]\end{gathered}
[
3
4
3
]
x [ 3 1 5 ]
u^T v = \begin{gathered}[\begin{array}{ccc}9&3&15\\12&4&20\\9&3&15\end{array}]\end{gathered}
[
9
12
9
3
4
3
15
20
15
]
Answer:
So the value of u^T v is \begin{gathered}[\begin{array}{ccc}9&3&15\\12&4&20\\9&3&15\end{array}]\end{gathered}
[
9
12
9
3
4
3
15
20
15
]