Linear Algebra Done Right: Solutions and Examples for Success

College
Algebra
Linear algebra

Let T denote the group of all nonsingular upper triaungular entries, i.e., the matrices of the form, [a,0,b,c] where $a, b, c \in H$
$H = {[1, 0, x, 1] \in T}$ is a normal subgroup of T.

snowlovelydayM 2021-01-13

Let $A = (1, 1, 1, 0), B = (- 1, 0, 1, 1,), C = (3, 2, - 1, 1)$
and let $D = {Q \in R^{4} | Q ⊥ A, Q ⊥ B, Q ⊥ C}$ .
Convince me that D is a subspace of $R^{4}$ . Write D as span of a basis. Write D as a span of an orthogonal basis

SchachtN 2021-01-13

Find the coordinates of T given that S is the midpoint of RT, R(2,6) and S(-2, 0).

ossidianaZ 2021-01-06

How are triple integrals defined in cylindrical and spherical coordinates?
Why might one prefer working in one of these coordinate systems to working in rectangular coordinates?

Kyran Hudson 2021-01-05

Find a set of vectors that spans the plane $P 1 : 2 x + 3 y - z = 0$

Yasmin 2021-01-05

Let S be a subset of an F-vector space V. Show that V is a subspace of Span(S).

jernplate8 2021-01-05

For each problem below, either prove that the mapping is linear or explain why it cannot be linear.
$1 . f (x_{1}, x_{2}) = (2 x_{1} - x_{2}, 3 x_{1} + x_{2})$
$2 . L (x, y, z) = (x + y, y + z, z + 5)$
$3 . L (x, y) = (x + y, 0, x - 2 y)$
$4 . f (x, y) = (2 x + y, - 3 x + 5 y)$
$5 . f (x, y) = (x^{2}, x + y)$
$6 . L (x, y) = (x, x + y, - y)$

Burhan Hopper 2021-01-04

The coefficient matrix for a system of linear differential equations of the form $y^{1} = A y$ has the given eigenvalues and eigenspace bases. Find the general solution for the system

$λ 1 = 3 \Rightarrow [\begin{matrix} 1 \\ 1 \\ 0 \end{matrix}]$

$λ 2 = 0 \Rightarrow [\begin{matrix} 1 \\ 5 \\ 1 \end{matrix}] [\begin{matrix} 2 \\ 1 \\ 4 \end{matrix}]$

facas9 2021-01-02

Find the angle between the vectors $< 1, 3 > and < - 2, 4 >$

Wotzdorfg 2021-01-02

To Sketch: The points on three - axis Cartesian coordinate system.
Point A: $[\begin{array}{ccc} - 6 & 2 & 1 \end{array}]$
Point B: $[\begin{array}{ccc} - 6 & 2 & 1 \end{array}]$
Point C: $[\begin{array}{ccc} 5 & - 3 & - 6 \end{array}]$

pedzenekO 2021-01-02

Write the vector v in the form ai + bj, given its magnitude ∥v∥∥v∥ and the angle $α$ it makes with the positive x-axis. $∥ v ∥= 8, α = 45 * ∥ v ∥= 8, α = 45$

chillywilly12a 2020-12-30

Let A := 5 1 16 -3 [2 3 9 4 (a) Find a basis for Nul A. (b) Find a basis for Col A.

Burhan Hopper 2020-12-30

Consider the elliptical-cylindrical coordinate system (eta, psi, z), defined by $x = a \cos h η \cos ψ, y = a \sin h η \sin ψ; z = z, η G E 0, 0 L E ψ L E 2 π, z R . I n P S 6$
it was shown that this is an orthogonal coordinate system with scale factors $h_{1} = h_{2} = a {({cosh}^{2} η - \cos^{2} ψ)}^{\frac{1}{2}} .$
Determine the dual bases $(E 1, E 2, E 3), (η, η ψ, z) . S h o w t \hat{:} f = a \frac{1}{a} \frac{{({cosh}^{2} e a t - \cos^{s} ψ)}^{1}}{2} [\frac{f}{η} e 1 + \frac{f}{ψ} e 2 + \frac{f}{z} e 3, \frac{f}{w} h e r e (e 1, e 2, e 3)$ denotes the unit coordinate basis.

Yulia 2020-12-30

Since we will be using various bases and the coordinate systems they define, let's review how we translate between coordinate systems. a. Suppose that we have a basis $B = {v_{1}, v_{2}, \dots, v_{m}} f or R^{m}$ . Explain what we mean by the representation {x}g of a vector x in the coordinate system defined by B. b. If we are given the representation ${x}_{B},$ how can we recover the vector x? c. If we are given the vector x, how can we find ${x}_{B}$ ? d. Suppose that BE is a basis for R^2. If $x_{B} = [\begin{matrix} 1 \\ - 2 \end{matrix}]$ find the vector x. e. If $x = [\begin{matrix} 2 \\ - 4 \end{matrix}] f i n d x_{B}$

Emily-Jane Bray 2020-12-29

The equivalent polar coordinates for the given rectangular coordinates:
$[\begin{array}{cc} 4 & 0 \end{array}]$

usagirl007A 2020-12-29

The systems used to find the location of the point in a plane and find the rectangular and polar coordinates for the point P.

boitshupoO 2020-12-28

How are triple integrals defined in cylindrical and spherical coor-dinates? Why might one prefer working in one of these coordinate systems to working in rectangular coordinates?

Burhan Hopper 2020-12-28

Assume that T is a linear transformation. Find the standard matrix of T.
$T = R^{2} \to R^{4} s u c h t h a t T (e_{1}) = (7, 1, 7, 1),$ .

$and T (e_{2}) = (- 8, 5, 0, 0), w h e r e e_{1} = (1, 0),$

$and e_{2} = (0, 1)$

Khadija Wells 2020-12-28

Write the vector form of the general solution of the given system of linear equations.
$x_{1} + 2 x_{2} - x_{3} = 0$
$x_{1} + x_{2} + x_{3} = 0$
$x_{1} + 3 x_{2} - 3 x_{3} = 0$

Tazmin Horton 2020-12-28

To compare and contrast: the rectangular, cylindrical and spherical coordinates systems.

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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