Show that C'[a, b] is subspace of C [a, b]

Kaycee Roche
2020-12-30
Answered

Show that C'[a, b] is subspace of C [a, b]

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asked 2021-02-11

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 2021-05-17

Find the scalar and vector projections of b onto a.

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

asked 2021-05-29

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)

asked 2021-05-29

Find a vector equation and parametric equations for the line segment that joins P to Q.

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

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

asked 2022-09-25

Let $F(x,y)=\u27e8-y,x\u27e9$ and C be the ellipse $\frac{{x}^{2}}{16}+\frac{{y}^{2}}{9}=1$ oriented counter clockwise, then find the value of ${\int}_{C}F.dr$

This is how I tried it,

$x=4\mathrm{cos}(t)\to dx=-4\mathrm{sin}(t)$

$y=3\mathrm{sin}(t)\to dy=3\mathrm{cos}(t)$

and $0\le t\le 2\pi $

${\int}_{C}F.dr=\int -ydx+xdy={\int}_{t=0}^{2\pi}12({\mathrm{sin}}^{2}(t)+{\mathrm{cos}}^{2}(t))dt=75.4$

But answer given to me at the back is 98.2 and doesn't agrees with mine.

This is how I tried it,

$x=4\mathrm{cos}(t)\to dx=-4\mathrm{sin}(t)$

$y=3\mathrm{sin}(t)\to dy=3\mathrm{cos}(t)$

and $0\le t\le 2\pi $

${\int}_{C}F.dr=\int -ydx+xdy={\int}_{t=0}^{2\pi}12({\mathrm{sin}}^{2}(t)+{\mathrm{cos}}^{2}(t))dt=75.4$

But answer given to me at the back is 98.2 and doesn't agrees with mine.

asked 2020-10-31

Imagine a rope tied around the Earth at the equator. Show that you need to add only feet of length to the rope in order to lift it one foot above the ground around the entire equator. (You do NOT need to know the radius of the Earth to show this.)

asked 2021-08-15

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