Linear Algebra Done Right: Solutions and Examples for Success

College
Algebra
Linear algebra

What is meant by resolution of a vector?

Jasmine Young 2023-01-06

How to find the determinant of a $2 \times 3$ matrix $?$

fatihahjohari18 2023-01-03

A positron under goes a displacement r=2i-3j+6k ending with the positron vectors r=3j-4k in meters.what was the positron initial positron vectors?

Memphis Burnett 2022-12-30

The equation of the horizontal line passing through the point (4,-7) is:
A)y−7=0
B)y+7=0
C)y−4=0
D)y+4=0

Kason Murray 2022-12-21

If two lines are perpendicular, then the product of their slope is _____.
A)0
B)1
C)-1
D)infinite

oxidricasbt7 2022-12-20

Eigenvalues of a $2 \times 2$ matrix A such that $A^{2} = I$
I have no idea where to begin.
I know there are a few matrices that support this claim, will they all have the same eigenvalues?

Jayden Davidson 2022-12-18

Can someone explain why a row replacement operation does not change the determinant of a matrix?

klepnin4wv 2022-12-18

Is the position a vector or scalar?

hrostent72t 2022-12-17

Which expression is equal to $- 3 b^{4} (6 b^{-} 8) ?$ Assume $b = / 0$

grapissosmfm 2022-12-17

_____ , is a characteristic of a linear function.
A.Graph has a constant slope
B.Graph does not have a constant slope
C.Graph always pass through the origin
D.Can't be determined

criminauiac 2022-12-14

What relationship does linear acceleration have with angular acceleration?

xuveirubvw 2022-12-10

The line that intersects two parallel lines is called a/an
A.Equivalent line
B.Transversal
C.Corresponding line
D.Origin line

Mariah Clark2022-12-05

The coordinates of the origin are ...........
A. (0, 1)
B.(0, 0)
C.(0, -1)
D.(1, 0)

e3r2a1cakCh7 2022-12-03

The matrix equation is not solved correctly. Expain the mistake and find the correct solution. Assume that the indicated inverses exist.
$X A = B, X = A^{- 1} B$

umthumaL3e 2022-12-02

With T defined by T(x)=Ax, find a vector x such that T(x)=b
$A = (\begin{matrix} 1 & - 3 & 2 \\ 3 & - 8 & 8 \\ 0 & 1 & 2 \\ 1 & 0 & 8 \end{matrix}), b = (\begin{matrix} 1 \\ 6 \\ 3 \\ 10 \end{matrix})$
What I have done so far is thatI have merged the two matrices into a single augmented matrix. And row reduced it to get:
$(\begin{matrix} 1 & - 3 & 2 & 1 \\ 0 & 1 & 2 & 3 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{matrix})$
So does this just mean that the answer to the question is $x = (\begin{matrix} 1 \\ 3 \\ 0 \\ 0 \end{matrix})$

Baardegem3Gw 2022-12-01

Find the orthogonal projection of a vector v onto U
Let $u$ be a unit vector in $R^{n}$ and let $U$ be the subspace spanned by $u$ . Show that the orthogonal projection of a vector $v$ onto $U$ is given by
${proj}_{U} v = (u u^{T}) v$
and thus that the matrix of this projection is $u u^{T}$ . What is the rank of $u u^{T}$ ?
Where $u^{T}$ is the transpose of $u$ . Any help is appreciate! I have no idea how to begin this other than knowing
${proj}_{U} v = \frac{(v, u) u}{(u, u)}$
Thanks!

Jay Park 2022-12-01

For vectors $\vec{u}, \vec{v}, \vec{w}$ and scalar $λ$
$1) \vec{w} \times \vec{v} = - (\vec{v} \times \vec{w}) 2) (λ \vec{v}) \times \vec{w} = λ (\vec{v} \times \vec{w}) = \vec{v} \times (λ \vec{w}) 3) \vec{u} \times (\vec{v} + \vec{w}) = \vec{u} \times \vec{v} + \vec{u} \times \vec{w}$
use the properties above which cross product properties
$((\vec{i} + \vec{j}) \times \vec{i}) \times \vec{j}$

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