Question

Compute ( x⋅x

x⋅w
​
)x using the vectors w= ⎣
⎡
​
3
−2
−5
​
⎦
⎤
​
and x= ⎣
⎡
​
6
−2
1
​
⎦
⎤
​
( x⋅x
x⋅w
​
)x= (Simplify your answer. Type an integer or simplified fraction for each matrix element.)

Answer 1

To compute (x⋅x)(x⋅w)x, we first need to calculate the dot product between vectors x and x, and between vectors x and w. Let's perform these calculations:

Dot product of x and x:

x⋅x = (6 * 6) + (-2 * -2) + (1 * 1)

= 36 + 4 + 1

= 41

Dot product of x and w:

x⋅w = (6 * 3) + (-2 * -2) + (1 * -5)

= 18 + 4 - 5

= 17

Now, we can substitute these values into the expression (x⋅x)(x⋅w)x:

(41 * 17) * x = (697) * x

Therefore, the result of (x⋅x)(x⋅w)x is 697 times the vector x.