Computing Inner Products of Vectors: a,b,c,d,e,f

[alkhaldi20]

Hi everyone,

I need help with this problem. I just can't get it:

Let a,b,c,d,e and f be vectors such that \langle a,b \rangle=-4, \quad \langle a,c \rangle=-9, \quad \langle b,c \rangle=2, \quad b+c=d, \quad -4 a+3 b=e and -4 b+5 c=f. Compute the following inner products:

\langle b,a \rangle=
\langle a,d \rangle=
\langle e,c \rangle=
\langle a,f \rangle=

 

[slider142]

Which question are you having trouble with? You have to apply the fact that the inner product is symmetric and linear in each argument. That is, for all vectors u, v, and w and all scalars a, we have:
$$\langle u, v\rangle = \langle v, u\rangle$$
and
$$\langle au + v, w\rangle = a\langle u, w\rangle + \langle v, w\rangle$$

 

[SammyS]

Hi everyone,

I need help with this problem. I just can't get it:

Let a,b,c,d,e and f be vectors such that $$\langle a,b \rangle=-4, \quad \langle a,c \rangle=-9, \quad \langle b,c \rangle=2, \quad b+c=d, \quad -4 a+3 b=e\ and -4 b+5 c=f\,.\$$

Compute the following inner products:

$$\langle b,a \rangle=$$
$$\langle a,d \rangle=$$
$$\langle e,c \rangle=$$
$$\langle a,f \rangle=$$

I put the $$\left[\text{tex}\right]\left[\text{/tex}\right]$$ tags in for you.

$$\langle a,d \rangle=\langle a,b+c \rangle=\langle a,b \rangle+\langle a,c \rangle=\,$$ etc.