Linear Algebra Done Right: Solutions and Examples for Success

College
Algebra
Linear algebra

Let n be a fixed positive integer greater thatn 1 and let a and b be positive integers. Prove that a mod n = b mon n if and only if a = b mod.

geduiwelh 2020-11-22

True or False? In Exercises 99 and 100, determine whether the statement is true or false. Justify your answer, : 99. The line through (−8,2) and (−1,4) and the line through (0,−4) and (−7,7) are parallel.

Jerold 2020-11-22

To find: The equivalent polar equation for the given rectangular-coordinate equation.
Given:
$x = r \cos θ$
$y = r \sin θ$
b. From rectangular to polar:
$r = \pm \sqrt{x^{2} + y^{2}}$
$\cos θ = \frac{x}{r}, \sin θ = \frac{y}{r}, \tan θ = \frac{x}{y}$
Calculation:
Given: equation in rectangular-coordinate is $y = x$ .
Converting into equivalent polar equation -
$y = x$
Put $x = r \cos θ, y = r \sin θ,$
$\Rightarrow r \sin θ = r \cos θ$
$\Rightarrow \frac{\sin θ}{\cos θ} = 1$
$\Rightarrow \tan θ = 1$
Thus, desired equivalent polar equation would be $θ = 1$

permaneceerc 2020-11-20

Find the angles made by the vectors $A = 5 i - 2 j + 3 k$ with the axes give a full correct answer

ka1leE 2020-11-20

Find the standard inner product on $P^{2}$ of the given polynomials $p = - 5 + 4 x + x^{2}, q = 3 + 4 x - 2 x^{2}$ .

waigaK 2020-11-17

The coordinates of the point in the $x^{'} y^{'}$ - coordinate system with the given angle of rotation and the xy-coordinates.

Phoebe 2020-11-16

Thealternate sets of representations for the points A-F from the Figure.

aortiH 2020-11-14

Consider the bases $B = (\begin{matrix} [\begin{matrix} 2 \\ 3 \end{matrix}], [\begin{matrix} 3 \\ 5 \end{matrix}] \end{matrix}) o f R^{2} a n d C = (\begin{matrix} [\begin{matrix} 1 \\ 1 \\ 0 \end{matrix}], [\begin{matrix} 1 \\ 0 \\ 1 \end{matrix}] \end{matrix}, [\begin{matrix} 0 \\ 1 \\ 1 \end{matrix}]) o f R^{3}$ .
and the linear maps $S \in L (R^{2}, R^{3}) a n d T \in L (R^{3}, R^{2})$ given given (with respect to the standard bases) by $[S]_{E, E} = [\begin{matrix} 2 & - 1 \\ 5 & - 3 \\ - 3 & 2 \end{matrix}] a n d [T]_{E, E} = [\begin{matrix} 1 & - 1 & 1 \\ 1 & 1 & - 1 \end{matrix}]$ Find each of the following coordinate representations. $(b) {[S]}_{E, C}$
$(c) {[S]}_{B, C}$

alesterp 2020-11-12

The given system of inequality:
${\begin{matrix} y < 9 - x^{2} \\ y \geq x + 3 \end{matrix}$
Also find the coordinates of all vertices, and check whether the solution set is bounded.

vazelinahS 2020-11-10

Consider the following linear transformation $T : P_{2} \to P_{3}$ , given by $T (f) = 3 x^{2} f$ '.

That is, take the first derivative and then multiply by $3 x^{2}$

(a) Find the matrix for T with respect to the standard bases of $P_{n}$ : that is, find $[T]_{ϵ}^{ϵ}$ , where- $ϵ = 1, x, x^{2}, x^{n}$

(b) Find N(T) and R(T). You can either work with polynomials or with their coordinate vectors with respect to the standard basis. Write the answers as spans of polynomials.

(c) Find the the matrix for T with respect to the alternate bases: $[T]_{A}^{B}$ where $A = x - 1, x, x^{2} + 1, B = x^{3}, x, x^{2}, 1 .$

snowlovelydayM 2020-11-10

Describe the translation of figure ABCD. Use the drop-down menus to explain your answer.
Figure ABCD is translated _ unit(s) right and __ unit(s) up.

jernplate8 2020-11-09

Prove that by setting these two expressions equal to another, the result is an identity:
$d = \cos^{- 1} (\sin (L T_{1}) \sin (L T_{2}) + \cos (L T_{1}) \cos (L T_{2}) \cos (\ln_{1} - \ln_{2}))$
$d = 2 \sin^{- 1} (\sqrt{\sin^{2} (\frac{L T_{1} - L T_{2}}{2}) + \cos (L T_{1}) \cos (L T_{2}) \sin^{2} (\frac{\ln_{1} - \ln_{2}}{2})})$

Ava-May Nelson 2020-11-08

The given matrix is the augmented matrix for a system of linear equations. Give the vector form for the general solution.
$[\begin{matrix} 1 & 0 & - 1 & - 2 \\ 0 & 1 & 2 & 3 \end{matrix}]$

Braxton Pugh 2020-11-08

Whether the statement "I need to be able to graph systems of linear inequalities in order to solve linear programming problems" makes sense or not.

banganX 2020-11-08

Prove that: If A or B is nonsingular, then AB is similar to BA

Trent Carpenter 2020-11-06

(i)Prove that if $v_{1}, v_{2}$ is linearly dependent, then are multiple of each other, that is, there exists a constant c such that $v_{1} = c v_{2} o r v_{2} = c v_{1}$ .
(ii)Prove that the converse of(i) is also true.That is to say, if there exists a constant c such that $v_{1} = c v_{2} o r v_{2} = c v_{1}$ , 1. then $v_{1}, v_{2}$ is linearly dependent.

Amari Flowers 2020-11-06

The line $2 x + 3 y = 8$ meets the curve $2 x^{2} + 3 y^{2} = 110$ at the points A and B.
Find the coordinates of A and B.

Chesley 2020-11-05

To graph: The sketch of the solution set of system of nonlinear inequality
$[x^{2} + y^{2} \geq 9]$
$x^{2} + y^{2} \leq 25$
$y \geq | x |$

Kaycee Roche 2020-11-05

To determine:
Find the sets of points in space whose coordinates satisfy the given combinations of equation and inequalities:
a) $y \geq x^{2}, z \geq 0,$
b) $x \leq y^{2}, 0 \leq z \leq 2 .$

Maiclubk 2020-11-03

Interraption: To show that the system $\dot{r} = r (1 - r^{2}), \dot{θ} = 1$ is equivalent to $\dot{x} = x - y - x (x^{2} + y^{2}), \dot{y} = x + y - y (x^{2} + y^{2})$ for polar to Cartesian coordinates.
A limit cycle is a closed trajectory. Isolated means that neighboring trajectories are not closed.
A limit cycle is said to be unstable or half stable, if all neighboring trajectories approach the lemin cycle.
These systems oscillate even in the absence of external periodic force.

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.

Linear algebra

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