Linear Algebra Done Right: Solutions and Examples for Success

College
Algebra
Linear algebra

Let $B = {v 1, v 2, \dots, v m}$ be a basis for $R^{m}$ . Suppose kvm is a linear combination of $v 1, v 2, \dots, v m - 1$ for some scalar k. What can be said about the possible value(s) of k?

sjeikdom0 2021-01-30

A line L through the origin in $R^{3}$ can be represented by parametric equations of the form x = at, y = bt, and z = ct. Use these equations to show that L is a subspase of $R R^{3}$ by showing that if $v_{1} = (x_{1}, y_{1}, z_{1}) a n d v_{2} = (x_{2}, y_{2}, z_{2})$ are points on L and k is any real number, then $k v_{1} a n d v_{1} + v_{2}$ are also points on L.

Jaden Easton 2021-01-28

The volume of the largest rectangular box which lies in the first octant with three faces in the coordinate planes and its one of the vertex in the plane $x + 2 y + 3 z = 6$ by using Lagrange multipliers.

banganX 2021-01-28

Given the vector $r (t) = \cos T, \sin T, \ln (\cos T)$ and point (1, 0, 0) find vectors T, N and B at that point.

Vector T is the unit tangent vector, so the derivative r(t) is needed.

Vector N is the normal unit vector, and the equation for it uses the derivative of T(t).

The B vector is the binormal vector, which is a crossproduct of T and N.

amanf 2021-01-28

Show that if u is a vector in R^{2} or R&3, then $u + (- 1) u = 0$
$u + (- 1) u = 0$

allhvasstH 2021-01-28

Find the Equivalent Polar Equation for a given Equation with Rectangular Coordinates:
$r \cos θ = - 1$

ankarskogC 2021-01-25

Let D be the diagonal subset $D = {(x, x) ∣ x \in S_{3}}$ of the direct product $S_{3} \times S_{3}$ . Prove that D is a subgroup of $S_{3} \times S_{3}$ but not a normal subgroup.

Dottie Parra 2021-01-25

Demonstrate that W is the collection of all $3 \times 3$ upper triangular matrices.
forms a subspace of all $3 \times 3$ matrices.
What is the dimension of W? Find a basis for W.

fortdefruitI 2021-01-24

It can be shown that the algebraic multiplicity of an eigenvalue lambda is always greater than or equal to the dimension of the eigenspace corresponding to lambda. Find h in the matrix A below such that the eigenspace for lambda = 5 is two-dimensional: $A = [\begin{array}{cccc} 5 & - 2 & 6 & - 1 \\ 0 & 3 & h & 0 \\ 0 & 0 & 5 & 4 \\ 0 & 0 & 0 & 1 \end{array}]$

aortiH 2021-01-23

To find: the distance between the lakes to the nearest mile.
Given:
(26,15) and (9,20)

Dottie Parra 2021-01-23

Give a correct answer for given question

(A) Argue why $(1, 0, 3), (2, 3, 1), (0, 0, 1)$ is a coordinate system ( bases ) for $R^{3}$ ?

(B) Find the coordinates of $(7, 6, 16)$ relative to the set in part (A)

Tolnaio 2021-01-23

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
$λ_{1} = 2 i \Rightarrow {[\begin{matrix} 1 + i \\ 2 - i \end{matrix}]}, λ_{2} = - 2 i \Rightarrow {[\begin{matrix} 1 - i \\ 2 + i \end{matrix}]}$

BolkowN 2021-01-23

Find basis and dimension ${x \in R^{4} ∣ x A = 0}$ where $A = {[- 1, 1, 2, 1, 1, 0, 2, 3]}^{T}$

Ava-May Nelson 2021-01-22

Whether the statement "If a system of two linear equations in two variables is dependent, then it has infinitely many solutions" is true or false.

texelaare 2021-01-22

Convert between the coordinate systems. Use the conversion formulas and show work. Spherical: $(8, \frac{π}{3}, \frac{π}{6})$ Change to cylindrical.

Falak Kinney 2021-01-22

Let $u = i + 2 j - 3 k$ and $v = 2 i + 3 j + k \in R^{3}$
(a) What is $u \cdot v$ ?
(b) What is $u \cdot v$ ?

smileycellist2 2021-01-19

Let $B = {[\begin{matrix} 1 \\ - 2 \end{matrix}], [\begin{matrix} 2 \\ 1 \end{matrix}]} a n d C = {[\begin{matrix} 2 \\ 1 \end{matrix}], [\begin{matrix} 1 \\ 3 \end{matrix}]}$
be bases for $R^{2} .$ Change-of-coordinate matrix from C to B.

glamrockqueen7 2021-01-19

Solve the following pair of linear equations by the elimination method and the substitution method:
$x + y = 5, 2 x - 3 y = 4$

zi2lalZ 2021-01-17

Let $v_{1}, v_{2}, \dots ., v_{k}$ be vectors of Rn such that
$v = c_{1} v_{1} + c_{2} v_{2} + \dots + c_{k} v_{k} = d_{1} v_{1} + d_{2} v_{2} + \dots + d_{k} v_{k}$ .
for some scalars $c_{1}, c_{2}, \dots ., c_{k}, d_{1}, d_{2}, \dots ., d_{k}$ .Prove that if $c i \neq d i f or s o m e i = 1, 2, \dots ., k$ ,
then $v_{1}, v_{2}, \dots ., v_{k}$ are linearly dependent.

rocedwrp 2021-01-15

It is given: $∥ m ∥= 4, ∥ n ∥= \sqrt{2}, ⟨ m, n ⟩ = 135$ find the norm of the vector $m + 3 n$ .

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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