Solved College Algebra Examples for Your Success

College
Algebra

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 $P^{n} \times P^{m}$ under the Segre embedding $ψ$ 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.
$X A = B, X = A^{- 1} B$

umthumaL3e 2022-12-02

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

ashley.dreyer 2022-12-01

Baardegem3Gw 2022-12-01

Find the orthogonal projection of a vector v onto U
Let $u$ 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
${proj}_{U} v = (u u^{T}) v$
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
${proj}_{U} v = \frac{(v, u) u}{(u, u)}$
Thanks!

Jay Park 2022-12-01

For vectors $\vec{u}, \vec{v}, \vec{w}$ and scalar $λ$
$1) \vec{w} \times \vec{v} = - (\vec{v} \times \vec{w}) 2) (λ \vec{v}) \times \vec{w} = λ (\vec{v} \times \vec{w}) = \vec{v} \times (λ \vec{w}) 3) \vec{u} \times (\vec{v} + \vec{w}) = \vec{u} \times \vec{v} + \vec{u} \times \vec{w}$
use the properties above which cross product properties
$((\vec{i} + \vec{j}) \times \vec{i}) \times \vec{j}$

Natalia Del Vecchio2022-11-30

Given that 1 $\log_{a} (3) \approx 0.61$ and l $\log_{a} (5) \approx 0.9$ , 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 $A = 4.8 \hat{i} + 6.6 \hat{j}, B = 5.9 \hat{i} + 5.1 \hat{j}$ . Find $A \times B$
$1) - 33.3 k 2) - 24.6 k 3) - 7.2 k 4) - 14.5 k 5) - 18.8 k$

quakbIi 2022-11-27

In triangles UVW and XYZ, U and Z are right angles, $U V ≅ \bar{Y Z}$ , and $\bar{V W} ≅ \bar{X Y}$ . 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
$\frac{x}{4} - \frac{3}{2} \leq \frac{x}{2} + 1$

Giovanna Shaw 2022-11-25

Why is distance not a vector quantity?

hEorpaigh3tR 2022-11-24

Generators of a free group
If 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 $P_{3}$ consisting of the Hermite polynomials $1, 2 t, - 2 + 4 t^{2}$ and $- 12 t + 8 t^{3}$ ; and let $p (t) = 1 + 16 t^{2} - 8 t^{3}$ . Find the coordinate vector of p relative to B.
$[p]_{B} = [\begin{matrix} - 7 \\ - 6 \\ - 4 \\ - 1 \end{matrix}]$

Ghennady Shyshakov2022-11-17

$C = \frac{5}{9} (F - 32)$
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 only
B) II only
C) III only
D) I and II only

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
$A = (\begin{matrix} 1 & 2 & 4 \\ 3 & 6 & 5 \end{matrix})$

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.

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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