# College Algebra Solutions for Your Success

Recent questions in Algebra
hEorpaigh3tR 2022-12-04

## The coordinates of the origin are ........... A. (0, 1) B.(0, 0) C.(0, -1) D.(1, 0)

Ghillardi4Pi 2022-12-04

## Show that the image of ${\mathbb{P}}^{n}×{\mathbb{P}}^{m}$ under the Segre embedding $\psi$ is actually irreducible.

e3r2a1cakCh7 2022-12-03

## The matrix equation is not solved correctly. Expain the mistake and find the correct solution. Assume that the indicated inverses exist. $XA=B,X={A}^{-1}B$

umthumaL3e 2022-12-02

## With T defined by T(x)=Ax, find a vector x such that T(x)=b$A=\left(\begin{array}{ccc}1& -3& 2\\ 3& -8& 8\\ 0& 1& 2\\ 1& 0& 8\end{array}\right)\phantom{\rule{2em}{0ex}},\phantom{\rule{2em}{0ex}}b=\left(\begin{array}{c}1\\ 6\\ 3\\ 10\end{array}\right)$What I have done so far is thatI have merged the two matrices into a single augmented matrix. And row reduced it to get:$\left(\begin{array}{cccc}1& -3& 2& 1\\ 0& 1& 2& 3\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right)$So does this just mean that the answer to the question is $\mathbf{x}=\left(\begin{array}{c}1\\ 3\\ 0\\ 0\end{array}\right)$

College algebraOpen question
ashley.dreyer 2022-12-01
Baardegem3Gw 2022-12-01

## Find the orthogonal projection of a vector v onto ULet $u$ be a unit vector in ${R}^{n}$ and let $U$ be the subspace spanned by $u$. Show that the orthogonal projection of a vector $v$ onto $U$ is given by${\mathrm{proj}}_{U}v=\left(u{u}^{T}\right)v$and thus that the matrix of this projection is $u{u}^{T}$. What is the rank of $u{u}^{T}$?Where ${u}^{T}$ is the transpose of $u$. Any help is appreciate! I have no idea how to begin this other than knowing${\mathrm{proj}}_{U}v=\frac{\left(v,u\right)u}{\left(u,u\right)}$Thanks!

Jay Park 2022-12-01

## For vectors $\stackrel{\to }{u},\stackrel{\to }{v},\stackrel{\to }{w}$ and scalar $\lambda$$1\right)\stackrel{\to }{w}×\stackrel{\to }{v}=-\left(\stackrel{\to }{v}×\stackrel{\to }{w}\right)\phantom{\rule{0ex}{0ex}}2\right)\left(\lambda \stackrel{\to }{v}\right)×\stackrel{\to }{w}=\lambda \left(\stackrel{\to }{v}×\stackrel{\to }{w}\right)=\stackrel{\to }{v}×\left(\lambda \stackrel{\to }{w}\right)\phantom{\rule{0ex}{0ex}}3\right)\stackrel{\to }{u}×\left(\stackrel{\to }{v}+\stackrel{\to }{w}\right)=\stackrel{\to }{u}×\stackrel{\to }{v}+\stackrel{\to }{u}×\stackrel{\to }{w}$use the properties above which cross product properties$\left(\left(\stackrel{\to }{i}+\stackrel{\to }{j}\right)×\stackrel{\to }{i}\right)×\stackrel{\to }{j}$

College algebraOpen question
Natalia Del Vecchio2022-11-30

## Given that 1${\mathrm{log}}_{a}\left(3\right)\approx 0.61$  and l${\mathrm{log}}_{a}\left(5\right)\approx 0.9$ , evaluate each of the following. Hint: use the properties of logarithms to rewrite the given logarithm in terms of the the logarithms of 3 and 5.

Jay Park 2022-11-29

## Define resultant vector.

FofieiyK 2022-11-29

## Two vectors are given by $A=4.8\stackrel{^}{i}+6.6\stackrel{^}{j},B=5.9\stackrel{^}{i}+5.1\stackrel{^}{j}$. Find $A×B$$1\right)-33.3k\phantom{\rule{0ex}{0ex}}2\right)-24.6k\phantom{\rule{0ex}{0ex}}3\right)-7.2k\phantom{\rule{0ex}{0ex}}4\right)-14.5k\phantom{\rule{0ex}{0ex}}5\right)-18.8k$

quakbIi 2022-11-27

## In triangles UVW and XYZ, U and Z are right angles, $UV\cong \overline{YZ}$, and $\overline{VW}\cong \overline{XY}$. Which theorem proves these triangles are congruent? A. HA Congruence Theorem B. LA Congruence Theorem C. LL Congruence Theorem D. None of these

Garrett Mclaughlin 2022-11-27

## Solve linear inequality$\frac{x}{4}-\frac{3}{2}\le \frac{x}{2}+1$

Giovanna Shaw 2022-11-25

## Why is distance not a vector quantity?

hEorpaigh3tR 2022-11-24

## Generators of a free groupIf G is a free group generated by n elements, is it possible to find an isomorphism of G with a free group generated by n-1 (or any fewer number) of elements?

Mollie Wise 2022-11-23

## Let B be the basis ${\mathbb{P}}_{3}$ consisting of the Hermite polynomials $1,2t,-2+4{t}^{2}$ and $-12t+8{t}^{3}$; and let $p\left(t\right)=1+16{t}^{2}-8{t}^{3}$. Find the coordinate vector of p relative to B.$\left[p{\right]}_{B}=\left[\begin{array}{c}-7\\ -6\\ -4\\ -1\end{array}\right]$

College algebraOpen question
Геннадий Шишаков2022-11-17

## $C=\frac{5}{9}\left(F-32\right)$The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?1. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of  $\frac{5}{9}$ degree Celsius.2. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.3. A temperature increase of $\frac{5}{9}$ degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.A) I onlyB) II onlyC) III onlyD) I and II only

AlgebraOpen question
Flame World2022-11-15

## Graph the polynomial function. Factor first if the expression is not in factored form.f(x)=x³+7x²+4x-12

atgnybo4fq 2022-11-12

## Determining the Rank of a Matrix$A=\left(\begin{array}{ccc}1& 2& 4\\ 3& 6& 5\end{array}\right)$

College algebraOpen question
Joe Dirt2022-11-10

## One of the two tables below shows data that can best be modeled by a linear function, and the other shows data that can best be modeled by a quadratic function. Identify which table shows the linear data and which table shows the quadratic data, and find a formula for each model.

College algebraOpen question
Joe Dirt2022-11-10

## One of the two tables below shows data that can best be modeled by a linear function, and the other shows data that can best be modeled by a quadratic function. Identify which table shows the linear data and which table shows the quadratic data, and find a formula for each model.

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