Solved College Algebra Examples for Your Success

College
Algebra

How many 3/4 Are in 1

Sai Ganesh naidu2022-10-10

Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs (0, 1),(1, 1),(1, 2),(2, 0),(2, 2),(3, 0). Find reflexive, symmetric and transitive closure of R.

shahed elhefni2022-10-08

Write an R function using Euclidean algorithm not only computes
the greatest common divisor d of a and b, but also two numbers s and t
such that d = s a + t b. (i.e solves Bezout's identity).

Krish Schmitt 2022-09-30

Suppose $V$ is a $n$ -dimensional linear vector space. ${s_{1}, s_{2}, . . ., s_{n}}$ and ${e_{1}, e_{2}, . . ., e_{n}}$ are two sets of orthonormal basis with basis transformation matrix $U$ such that $e_{i} = \sum_{j} U_{i j} s_{j}$ .
Now consider the $n^{2}$ dim vector space $V ⨂ V$ (kronecker product) with equivalent basis sets ${s_{1} s_{1}, s_{1} s_{2}, . . ., s_{n} s_{n}}$ and ${e_{1} e_{1}, e_{1} e_{2}, . . ., e_{n} e_{n}}$ . Now can we find the basis transformation matrix for this in terms of U?

kolbergkd 2022-09-29

nikhil mamillpalli2022-09-27

draw the hasse diagram representing the partial ordering {(a,b)|a<=b} on {1,2,3,4,6,8,12},is it a lattice justify

samphacc 2022-09-27

Triangle J K L is shown. The length of J K is 13, the length of K L is 11, and the length of L J is 19.Law of cosines: a2 = b2 + c2 – 2bccos(A)

Find the measure of AngleJ, the smallest angle in a triangle with sides measuring 11, 13, and 19. Round to the nearest whole degree.

30°
34°
42°
47°

Chelsea Lamb 2022-09-26

If the matrix of a linear transformation $: R^{N} \to R^{N}$ with respect to some basis is symmetric, what does it say about the transformation? Is there a way to geometrically interpret the transformation in a nice/simple way?

Topniveauh2 2022-09-25

Convert 10 meters to feet. Round your answer to the nearest tenth

Julia Chang 2022-09-25

Give the standard matrix of the linear transformation that first sends (x, y, z) to (y, y, z), and rotates this vector 90 degrees counterclockwise about the origin in the x = y plane. Find standard matrix of linear transformation.

Colten Andrade 2022-09-21

Given a matrix $Y \in R^{m \times n}$ . Find a transformation matrix $Θ \in R^{n \times p}$ such that
$\frac{1}{m} Θ^{T} Y^{T} Y Θ = I_{p \times p},$
where 𝐼𝑝×𝑝 is identity matrix.
My attempt: $\frac{1}{\sqrt{m}} Y Θ$ is orthogonal matrix and tried to find $Θ$ satisfies it but that doesn't work.

Celinamg8 2022-09-20

Vector, $u := [u_{1}, \dots, u_{n}]^{T}$ . I am trying to find a coordinate transformation matrix, $Q \in R^{n \times n}$ , which is nonsingular, satisfying:
$\begin{aligned} [\begin{matrix} 0 \\ ⋮ \\ 0 \\ | | u | | \end{matrix}] = Q u . \end{aligned}$

ahmed zubair2022-09-14

A trust fund has $200,000 to invest. Three alternative investments have been identified, earning income of 10 percent, 7 percent and 8 percent respectively. A goal has been set to earn an annual income of $16,000 on the total investment. One condition set by the trust is that the combine investment in alternatives 2 and 3 should be triple the amount invested in alternative 1. Determine the amount of money, which should be invested in each option to satisfy the requirements of the trust fund. Solve by Gauss- Jordon method

What are the equations formed in this question?

nar6jetaime86 2022-09-13

Findthe Matrix T of the following linear transformation
$T : R 2 (x) - > R 2 (x) d e f i n e d b y T (a x^{2} + b x + c) = 2 a x + b$

tamola7f 2022-09-13

Every matrix represents a linear transformation, but depending on characteristics of the matrix, the linear transformation it represents can be limited to a specific type. For example, an orthogonal matrix represents a rotation (and possibly a reflection). Is it something similar about triangular matrices? Do they represent any specific type of transformation?

Julius Blankenship 2022-09-12

Consider $K^{n}$ , $K^{m}$ , both with the $| | . | |_{1}$ -norm, where $K = R$ or $C$ .
Let $| | T | | = i n f {M \geq 0 : | | T (x) | | \leq M | | x | | \forall x \in K^{n}}$ be the operator norm of a linear transformation $T : K^{n} \to K^{m}$ .
Show that the operator norm of the linear transformation $T$ is also given by:
$| | T | | = m a x {\sum_{i = 1}^{m} | a_{i j} |, 1 \leq j \leq n} =: | | A | |_{1}$
where $A$ is the transformation matrix of $T$ and $a_{i j}$ it's entry in the $i$ -th row and $j$ -the column.

Addison Parker 2022-09-12

Without constructing, find the coordinates of the points of intersection of the graph of the function y = -0.6x + 3 with the coordinate axes.

Amy Kurtz2022-09-11

A baseball team plays in a stadium that holds 70,000 spectators. With the ticket price at $11, the average attendance has been 29,000. When the price dropped to $10, the average attendance rose to 35,000. Assuming the demand function, p(x) $p (x)$ , is linear, find p(x) $p (x)$ , where x $x$ is the number of the spectators. Write p(x) $p (x)$ in slope-intercept form.

engausidarb 2022-09-11

Real symmetric matrices $S_{i j}$ can always be put in a standard diagonal form $s_{i} δ_{i j}$ under an orthogonal transformation. Similarly, real antisymmetric matrices $A_{i j}$ can always be put in a standard band diagonal form with diagonal matrix entries $a_{i} (\begin{matrix} 0 & 1 \\ - 1 & 0 \end{matrix})$ (with a $0$ diagonal entry when the dimension of the matrix is odd), again under an orthogonal transformation.

tuzkutimonq4 2022-09-11

Convert the following matrix:
$[\begin{matrix} 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \end{matrix}]$
To the following:
$[\begin{matrix} 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 \\ 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \end{matrix}]$

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College Algebra Solutions for Your Success