Linear Algebra Done Right: Solutions and Examples for Success

College
Algebra
Linear algebra

Determine whether the given $(2 \times 3) (2 \times 3)$ system of linear equations represents coincident planes (that is, the same plane), two parallel planes, or two planes whose intersection is a line. In the latter case, give the parametric equations for the line, that is, give equations of the form
$x = a t + b, y = c t + d, z = e t + f$
$2 x_{1} + x_{2} + x_{3} = 3$
$- 2 x_{1} + x_{2} - x_{3} = 1$

chillywilly12a 2021-02-09

Determine if
$a . H = {\frac{x, y}{y} = 3 x - 1}$ is a subspace of R2
$b . H = {a t + \frac{b}{b} = 8 a}$ is a subspace of P1

Wierzycaz 2021-02-09

To determine:
a) Whether the statement, " The point with Cartesian coordinates $[\begin{array}{cc} - 2 & 2 \end{array}]$ has polar coordinates $[b f (2 \sqrt{2}, \frac{3 π}{4}) (2 \sqrt{2}, \frac{11 π}{4}) (2 \sqrt{2}, - \frac{5 π}{4}) and (- 2 \sqrt{2}, - \frac{π}{4})]$ " is true or false.
b) Whether the statement, " the graphs of $[r \cos θ = 4 and r \sin θ = - 2]$ intersect exactly once " is true or false.
c) Whether the statement, " the graphs of $[r = 4 and θ = \frac{π}{4}]$ intersect exactly once ", is true or false.
d) Whether the statement, " the point $[\begin{array}{cc} 3 & \frac{π}{2} \end{array}] l i e s o n t h e g r a p h o f [r = 3 \cos 2 θ]$ " is true or false.
e) Whether the statement, " the graphs of $[r = 2 \sec θ and r = 3 \csc θ]$ are lines " is true or false.

Sinead Mcgee 2021-02-08

Let $β = (x^{2} - x, x^{2} + 1, x - 1), β^{'} = (x^{2} - 2 x - 3, - 2 x^{2} + 5 x + 5, 2 x^{2} - x - 3)$ be ordered bases for $P_{2} (C) .$ Find the change of coordinate matrix Q that changes $β^{'}$ -coordinates into $β$ -coordinates.

nagasenaz 2021-02-08

m Find m $Y = (6 x + 44)$
$Z = (- 10 x + 65)$

Emeli Hagan 2021-02-08

Find the distance UV between the points U(7,−4) and V(−3,−6). Round your answer to the nearest tenth, if neces

Kaycee Roche 2021-02-08

Determine the area under the standard normal curve that lies between
(a) Upper Z equals -2.03 and Upper Z equals 2.03,
(b) Upper Z equals -1.56 and Upper Z equals 0, and
(c) Upper Z equals -1.51 and Upper Z equals 0.68.

Kyran Hudson 2021-02-08

To find: The equivalent polar equation for the given rectangular-coordinate equation.
Given:
$x^{2} + y^{2} + 8 x = 0$

bobbie71G 2021-02-08

Write an augumented matrix for the system of linear equations
$[\begin{matrix} x - y + z = 8 \\ y - 12 z = - 15 \\ z = 1 \end{matrix}]$

babeeb0oL 2021-02-08

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

preprekomW 2021-02-06

1:Find the determinant of the following mattrix $[\begin{matrix} \begin{matrix} 2 & - 1 & - 6 \end{matrix} \\ \begin{matrix} - 3 & 0 & 5 \end{matrix} \\ \begin{matrix} 4 & 3 & 0 \end{matrix} \end{matrix}]$

2: If told that matrix A is singular Matrix find the possible value(s) for x $A = {\begin{matrix} 16 x & 4 x \\ x & 9 \end{matrix}$

Mylo O'Moore 2021-02-06

A vector is first rotated by $90^{\circ}$ along x-axis and then scaled up by 5 times is equal to $(15, - 10, 20)$ . What was the original vector

tinfoQ 2021-02-05

Provide notes on how triple integrals defined in cylindrical and spherical coordinates and the reason to prefer one of these coordinate systems to working in rectangular coordinates.

Ava-May Nelson 2021-02-05

Given point P(-2, 6, 3) and vector $B = y a_{x} + (x + z) a_{y}$ , express P and B in cylindrical and spherical coordinates. Evaluate A at P in the Cartesian, cylindrical and spherical systems.

midtlinjeg 2021-02-03

Explain the difference between Alternating Direction Method of Multipliers(ADMM) and coordinate descent (CD) .

Tyra 2021-02-03

Determine whether the given $(2 \times 3)$ system of linear equations represents coincident planes (that is, the same plane), two parallel planes, or two planes whose intersection is a line. In the latter case, give the parametric equations for the line, that is, give equations of the form
$x = a t + b, y = c t + d, z = e t + f .$
$x_{1} + 2 x_{2} - x_{3} = 2$
$x_{1} + x_{2} + x_{3} = 3$

Yasmin 2021-02-02

Suppose the vertices of the original figure in the example were A(-6,6), B(-2,5), and C(-6,2). What would be the vertices of the image after a 90° clockwise rotation about the origin?
A'()
B'()
C'(___)

BolkowN 2021-01-31

The quadratic function $y = a x^{2} + b x + c$ whose graph passes through the points (1, 4), (2, 1) and (3, 4).

Emeli Hagan 2021-01-31

(10%) In $R^{2}$ , there are two sets of coordinate systems, represented by two distinct bases: $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ . If the equations of the same ellipse represented by the two distinct bases are described as follows, respectively: $2 (x_{1})^{2} - 4 (x_{1}) (y_{1}) + 5 (y_{1})^{2} - 36 = 0$ and $(x_{2})^{2} + 6 (y_{2})^{2} - 36 = 0.$ Find the transformation matrix between these two coordinate systems: $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

ossidianaZ 2021-01-31

(a) Find the bases and dimension for the subspace $H = {[\begin{matrix} 3 a + 6 b - c \\ 6 a - 2 b - 2 c \\ - 9 a + 5 b + 3 c \\ - 3 a + b + c \end{matrix}]; a, b, c \in R}$ (b) Let be bases for a vector space V,and suppose (i) Find the change of coordinate matrix from B toD. (ii) Find ${[x]}_{D} f or x = 3 b_{1} - 2 b_{2} + b_{3}$

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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