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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.)

User KibGzr
by
8.1k points

1 Answer

3 votes

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.

User Maxter
by
7.5k points