Linear Algebra Done Right: Solutions and Examples for Success

College
Algebra
Linear algebra

Let the vector space $P^{2}$
have the inner product $⟨ p, q ⟩ = \int_{- 1}^{1} p (x) q (x) d x .$
Find the following for $p = 1 a n d q = x^{2} .$
$(a) ⟨ p, q ⟩ (b) ∥ p ∥ (c) ∥ q ∥ (d) d (p, q)$

Anish Buchanan 2021-03-12

Let $A = [\begin{matrix} a & b \\ c & d \end{matrix}]$ and 'k' be the scalar. Find the formula that relates 'detKA' to 'K' and 'detA''

beljuA 2021-03-11

Find all scalars $c_{1}, c_{2}, c_{3}$ such that $c_{1} (1, - 1, 0) + c_{2} (4, 5, 1) + c_{3} (0, 1, 5) = (3, 2, - 19)$

SchachtN 2021-03-08

The position vector $r (t) = ⟨ \ln t, \frac{1}{t^{2}}, t^{4} ⟩$ describes the path of an object moving in space.
(a) Find the velocity vector, speed, and acceleration vector of the object.
(b) Evaluate the velocity vector and acceleration vector of the object at the given value of $t = \sqrt{3}$

Braxton Pugh 2021-03-08

A city planner wanted to place the new town library at site A. The mayor thought that it would be better at site B. What transformations were applied to the building at site A to relocate the building to site B? Did the mayor change the size or orientation of the library?
[Pic]

a2linetagadaW 2021-03-07

Give the elementary matrix that converts
$[\begin{matrix} - 2 & - 2 & - 1 \\ - 3 & - 1 & - 3 \\ 1 & - 4 & - 3 \end{matrix}]$

to

$[\begin{matrix} - 6 & - 2 & - 1 \\ - 5 & - 1 & - 3 \\ - 7 & - 4 & - 3 \end{matrix}]$

glasskerfu 2021-03-07

Find the value of x or y so that the line passing through the given points has the given slope. (9, 3), (-6, 7y), $m = 3$

smileycellist2 2021-03-04

Write the homogeneous system of linear equations in the form AX = 0. Then verify by matrix multiplication that the given matrix X is a solution of the system for any real number $c_{1}$
${\begin{cases} x_{1} + x_{2} + x_{3} + x_{4} = 0 \\ - x_{1} + x_{2} - x_{3} + x_{4} = 0 \\ x_{1} + x_{2} - x_{3} - x_{4} = 0 \\ 3 x_{1} + x_{2} + x_{3} - x_{4} = 0 \end{cases}$
$X = (\begin{matrix} 1 \\ - 1 \\ - 1 \\ 1 \end{matrix})$

bobbie71G 2021-03-04

use the Laplace transform to solve the given initial-value problem.
$y " + y = f (t)$
$y (0) = 0, y^{'} (0) = 1$ where
$f (t) = {\begin{matrix} 1 & 0 \leq t < \frac{π}{2} \\ 0 & t \geq \frac{π}{2} \end{matrix}$

e1s2kat26 2021-03-04

Show that $C^{} = R_{+}^{} \times T, where C^{}$ is the multiplicative group of non-zero complex numbers, T is the group of complex numbers of modulus equal to 1, $R_{+}^{}$ is the multiplicative group of positive real numbers.

Suman Cole 2021-03-02

To plot: Thepoints which has polar coordinate $(2, \frac{7 π}{4})$ also two alternaitve sets for the same.

Jaya Legge 2021-03-02

Let U,V be subspaces of Rn. Suppose that $U ⊥ V .$ Prove that ${u, v}$ is linearly independent for any nonzero vectors $u \in U, v \in V .$

fortdefruitI 2021-03-02

Let u, $v_{1}$ and $v_{2}$ be vectors in $R^{3}$ , and let $c_{1}$ and $c_{2}$ be scalars. If u is orthogonal to both $v_{1}$ and $v_{2}$ , prove that u is orthogonal to the vector $c_{1} v_{1} + c_{2} v_{2}$ .

babeeb0oL 2021-03-02

Let T be the linear transformation from R2 to R2 consisting of reflection in the y-axis. Let S be the linear transformation from R2 to R2 consisting of clockwise rotation of $30^{\circ}$ . (b) Find the standard matrix of $T, [T]$ . See p. 216 and, more generally, section 3.6 of your text if you're unsure of what this is.

alesterp 2021-03-02

Use $A B \leftarrow\to$ and $C D \leftarrow\to$ to answer the question. $A B \leftarrow\to$ contains the points A(2,1) and B(3,4). $C D \leftarrow\to$ contains the points C(−2,−1) and D(1,−2). Is $A B \leftarrow\to$ perpendicular to $C D \leftarrow\to$ ? Why or why not?

coexpennan 2021-03-01

Write an equation of the line that passes through (3, 1) and (0, 10)

Reggie 2021-02-27

The system of equation ${\begin{cases} 2 x + y = 1 \\ 4 x + 2 y = 3 \end{cases}$ by graphing method and if the system has no solution then the solution is inconsistent.
Given: The linear equations is ${\begin{cases} 2 x + y = 1 \\ 4 x + 2 y = 3 \end{cases}$

djeljenike 2021-02-27

What are polar coordinates? What equations relate polar coordi-nates to Cartesian coordinates? Why might you want to change from one coordinate system to the other?

Cheyanne Leigh 2021-02-26

The reason ehy the point $(- 1, \frac{3 π}{2})$ lies on the polar graph $r = 1 + \cos θ$ even though it does not satisfy the equation.

Tazmin Horton 2021-02-26

The equivalent polar equation for the given rectangular - coordinate equation.
$y = - 3$

Finding detailed linear algebra problems and solutions has always been difficult because the textbooks would never provide anything that would be sufficient. Since it is used not only by engineering students but by anyone who has to work with specific calculations, we have provided you with a plethora of questions and answers in their original form. It will help you to see some logic as you are solving complex numbers and understand the basic concepts of linear Algebra in a clearer way. If you need additional help or would like to connect several solutions, compare more than one solution as you approach your task.

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