a)

b)

c)

d)

e)

f)

chillywilly12a
2021-05-29
Answered

Which of the following expressions are meaningful? Which are meaningless? Explain.

a)$(a\cdot b)\cdot c$

$(a\cdot b)\cdot c$ has ? because it is the dot product of ?.

b)$(a\cdot b)c$

$(a\cdot b)c$ has ? because it is a scalar multiple of ?.

c)$|a|(b\cdot c)$

$|a|(b\cdot c)$ has ? because it is the product of ?.

d)$a\cdot (b+c)$

$a\cdot (b+c)$ has ? because it is the dot product of ?.

e)$a\cdot b+c$

$a\cdot b+c$ has ? because it is the sum of ?.

f)$|a|\cdot (b+c)$

$|a|\cdot (b+c)$ has ? because it is the dot product of ?.

a)

b)

c)

d)

e)

f)

You can still ask an expert for help

Clara Reese

Answered 2021-05-30
Author has **120** answers

Step 1

a) The expression

Note that here, the dot product

b) The expression

Note that here, the dot product

c) The expression

Here, two scalars can be multiplied easily.

d) The expression

Note that here, the sum of two vectors,

e) The expression

Note that, a scalar and a vector cannot be added.

f) The expression

Note that, a scalar and a vector cannot be dot product with each other.

asked 2021-05-29

Find the vector and parametric equations for the line segment connecting P to Q.

P(0, - 1, 1), Q(1/2, 1/3, 1/4)

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Find the scalar and vector projections of b onto a.

$a=(4,7,-4),b=(3,-1,1)$

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Let F be a fixed 3x2 matrix, and let H be the set of all matrices A in $M}_{2\times 4$ with the property that FA = 0 (the zero matrix in ${M}_{3\times 4})$ . Determine if H is a subspace of $M}_{2\times 4$

asked 2022-10-30

I have a function ${s}^{T}{x}_{i}{x}_{j}^{T}s$ where $s\in {\mathbf{R}}^{\mathbf{d}}$ and $x\in {\mathbf{R}}^{\mathbf{d}}$ which is computed at every index of matrix which means ${K}_{ij}={s}^{T}{x}_{i}{x}_{j}^{T}s$ with ${K}_{ij}\in {\mathbf{R}}^{\mathbf{n}\mathbf{\text{}}\mathbf{x}\mathbf{\text{}}\mathbf{n}}$. Now if i take any vector $v\in {\mathbf{R}}^{\mathbf{n}}$ then how to multiply that vector with matrix with matrix in this form ${v}^{T}.K.v$. What I have done so far is

$\sum _{i,j}{z}_{i}.({s}_{i}.{x}_{i}.{x}_{j}.{s}_{j}).{z}_{j}$

Is it possible to complete the square of the above term with the one given below?

$\sum _{i}||{z}_{i}.{s}_{i}.{x}_{i}|{|}^{2}$

$\sum _{i,j}{z}_{i}.({s}_{i}.{x}_{i}.{x}_{j}.{s}_{j}).{z}_{j}$

Is it possible to complete the square of the above term with the one given below?

$\sum _{i}||{z}_{i}.{s}_{i}.{x}_{i}|{|}^{2}$

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Find the angle $\theta$ between the given vectors to the nearest tenth of a degree.

$U=-5i+7j,\text{}V=8i+3j$

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Will a vector rotate back to itself under unitary rotation?

Let there be an arbitrary complex vector $\overrightarrow{v}\in {\mathbb{C}}^{D}$ that has unit length defined as $\sum _{i}{v}_{i}{v}_{i}^{\ast}=1$. Let there be a Hermitian $D\times D$ matrix H. Given arbitrary $\overrightarrow{v}$ and H, will there always exist a non-zero $t\in \mathbb{R}$ such that ${e}^{iHt}\overrightarrow{v}=\overrightarrow{v}$?

Let there be an arbitrary complex vector $\overrightarrow{v}\in {\mathbb{C}}^{D}$ that has unit length defined as $\sum _{i}{v}_{i}{v}_{i}^{\ast}=1$. Let there be a Hermitian $D\times D$ matrix H. Given arbitrary $\overrightarrow{v}$ and H, will there always exist a non-zero $t\in \mathbb{R}$ such that ${e}^{iHt}\overrightarrow{v}=\overrightarrow{v}$?

asked 2022-10-21

If a,b,c are three non coplanar vectors, then prove that the vector equation

$r=(1-p-q)\overrightarrow{a}+p\overrightarrow{b}+q\overrightarrow{c}$ represents a plane

Let $r=x\overrightarrow{a}+y\overrightarrow{b}+z\overrightarrow{c}$

Comparing with the given equation, we obtain

x+y+z=1

which is a plane

What I don’t understand is how does this say r is a plane, since r is actually $x\overrightarrow{a}+y\overrightarrow{b}+z\overrightarrow{c}$

$r=(1-p-q)\overrightarrow{a}+p\overrightarrow{b}+q\overrightarrow{c}$ represents a plane

Let $r=x\overrightarrow{a}+y\overrightarrow{b}+z\overrightarrow{c}$

Comparing with the given equation, we obtain

x+y+z=1

which is a plane

What I don’t understand is how does this say r is a plane, since r is actually $x\overrightarrow{a}+y\overrightarrow{b}+z\overrightarrow{c}$