# Linear algebra questions and answers

Recent questions in Linear algebra
texelaare 2020-11-01

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

Jason Farmer 2020-11-01

### The equivalent polar coordinates for the given rectangular coordinates. A rectangular coordinate is given as (0, -3).

CoormaBak9 2020-11-01

### Give a full correct answer for given question 1- Let W be the set of all polynomials $a+bt+c{t}^{2}\in {P}_{2}$ such that $a+b+c=0$ Show that W is a subspace of ${P}_{2},$ find a basis for W, and then find dim(W) 2 - Find two different bases of ${R}^{2}$ so that the coordinates of $b=\left[\begin{array}{c}5\\ 3\end{array}\right]$ are both (2,1) in the coordinate system defined by these two bases

nagasenaz 2020-11-01

### To calculate: The intercepts on the coordinate axes of the straight line with the given equation $2y-4=3x$

geduiwelh 2020-11-01

### class council determined that its profit from the upcoming homecoming dance is directly related to the ticket price for the dance. Looking at past dances, the council determined that the profit pp can be modeled by the function $p\left(t\right)=-12{t}^{2}+480t+30$, where tt represents the price of each ticket. What should be the price of a ticket to the homecoming dance to maximize the council's profit? Price

e1s2kat26 2020-11-01

### Let $\gamma =\left\{{t}^{2}-t+1,t+1,{t}^{2}+1\right\}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\beta =\left\{{t}^{2}+t+4,4{t}^{2}-3t+2,2{t}^{2}+3\right\}be\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}deredbasesf\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}{P}_{2}\left(R\right).$ Find the change of coordinate matrix Q that changes

Cheyanne Leigh 2020-11-01

### Given f(x)=6x+5​, describe how the graph of g compares with the graph of f. g(x)=6(0.2x)+5 Select the correct choice below, and fill in the answer box to complete your choice. A. The graph of​ g(x) is translated _ ​unit(s) to the left compared to the graph of​ f(x). B. The graph of​ g(x) is translated _ ​unit(s) down compared to graph of​ f(x). C. g(x) has a scale factor of _ compared to​ f(x). Because it scales the vertical​ direction, the graph is stretched vertically. D. g(x) has a scale factor of _ compared to​ f(x). Because it scales the vertical​ direction, the graph is compressed vertically. E. g(x) has a scale factor of _ compared to​ f(x). Because it scales the horizontal​ direction, the graph is stretched horizontally. F. g(x) has a scale factor of _ compared to​ f(x). Because it scales the horizontal​ direction, the graph is compressed horizontally. G. The graph of​ g(x) is translated _ ​unit(s) to the right compared to the graph of​ f(x). H. The graph of​ g(x) is translated _ ​unit(s) up compared to graph of​ f(x).

Lennie Carroll 2020-10-28

### [Pic] Describe a combination of transformations.

tricotasu 2020-10-26

### A line passes through (9,3),(12,4), and (n,-5) Find the value of n.

CoormaBak9 2020-10-25

### Let B and C be the following ordered bases of ${R}^{3}:$ $B=\left(\left[\begin{array}{c}1\\ 4\\ -\frac{4}{3}\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 8\end{array}\right],\left[\begin{array}{c}1\\ 1\\ -2\end{array}\right]\right)$ $C=\left(\left[\begin{array}{c}1\\ 1\\ -2\end{array}\right],\left[\begin{array}{c}1\\ 4\\ -\frac{4}{3}\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 8\end{array}\right]\right)$ Find the change of coordinate matrix I_{CB}

Brennan Flores 2020-10-21

### Find the Euclidean distance between u and v and the cosine of the angle between those vectors. State whether that angle is acute, obtuse, or ${90}^{\circ }$. u = (-1, -1, 8, 0), v = (5,6,1,4)

waigaK 2020-10-21

### Consider the following vectors in ${R}^{4}:$ ${v}_{1}=\left[\begin{array}{c}1\\ 1\\ 1\\ 1\end{array}\right],{v}_{2}=\left[\begin{array}{c}0\\ 1\\ 1\\ 1\end{array}\right]{v}_{3}=\left[\begin{array}{c}0\\ 0\\ 1\\ 1\end{array}\right],{v}_{4}=\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]$ d. If $x=\left[\begin{array}{c}23\\ 12\\ 10\\ 19\end{array}\right],find{\left\{x\right\}}_{B}e$. If ${x}_{B}=\left[\begin{array}{c}3\\ 1\\ -4\\ -4\end{array}\right]$, find x.

necessaryh 2020-10-21

### For any vectors u, v and w, show that the vectors u-v, v-w and w-u form a linearly dependent set.

Jason Farmer 2020-10-21

### The image of the point (2,1) under a translation is (5,-3). Find the coordinates of the image of the point (6,6) under the same translation.

Lennie Carroll 2020-10-20

### Consider the linear transformation $U:{R}^{3}\to {R}^{3}$ defined by $U\left(\begin{array}{c}x\\ y\\ z\end{array}\right)=\left(\begin{array}{c}z-y\\ z+y\\ 3z-x-y\end{array}\right)$ and the bases $ϵ=\left\{\left(\begin{array}{c}1\\ 0\\ 0\end{array}\right),\left(\begin{array}{c}0\\ 1\\ 0\end{array}\right),\left(\begin{array}{c}0\\ 0\\ 1\end{array}\right)\right\},\gamma =\left\{\left(\begin{array}{c}1-i\\ 1+i\\ 1\end{array}\right),\left(\begin{array}{c}-1\\ 1\\ 0\end{array}\right),\left(\begin{array}{c}0\\ 0\\ 1\end{array}\right)\right\}$, Compute the four coordinate matrices ${\left[U\right]}_{ϵ}^{\gamma },{\left[U\right]}_{\gamma }^{\gamma },$

tinfoQ 2020-10-18

### Find the vector and parametric equations for the line through the point P=(5,−2,3) and the point Q=(2,−7,8).

illusiia 2020-10-18

### Given the full and correct answer the two bases of $B1=\left\{\left(\begin{array}{c}2\\ 1\end{array}\right),\left(\begin{array}{c}3\\ 2\end{array}\right)\right\}$ ${B}_{2}=\left\{\left(\begin{array}{c}3\\ 1\end{array}\right),\left(\begin{array}{c}7\\ 2\end{array}\right)\right\}$ find the change of basis matrix from ${B}_{1}\to {B}_{2}$ and next use this matrix to covert the coordinate vector ${\stackrel{\to }{v}}_{{B}_{1}}=\left(\begin{array}{c}2\\ -1\end{array}\right)$ of v to its coodirnate vector ${\stackrel{\to }{v}}_{{B}_{2}}$

Wribreeminsl 2020-10-18

### Given the elow bases for ${R}^{2}$ and the point at the specified coordinate in the standard basis as below, (40 points) $\left(B1=\left\{\left(1,0\right),\left(0,1\right)\right\}$& $B2=\left(1,2\right),\left(2,-1\right)\right\}$(1, 7) = ${3}^{\ast }\left(1,2\right)-\left(2,1\right)$ $B2=\left(1,1\right),\left(-1,1\right)\left(3,7={5}^{\ast }\left(1,1\right)+{2}^{\ast }\left(-1,1\right)$ $\left(8,10\right)={4}^{\ast }\left(1,2\right)+{2}^{\ast }\left(2,1\right)$ B2 = (1, 2), (-2, 1) (0, 5) = (1, 7) = a. Use graph technique to find the coordinate in the second basis. (10 points) b. Show that each basis is orthogonal. (5 points) c. Determine if each basis is normal. (5 points) d. Find the transition matrix from the standard basis to the alternate basis. (15 points)

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.