 # Linear algebra questions and answers

Recent questions in Linear algebra snowlovelydayM 2020-11-10 Answered

### Describe the translation of figure ABCD. Use the drop-down menus to explain your answer. Figure ABCD is translated _____ unit(s) right and ______ unit(s) up. vazelinahS 2020-11-10 Answered

### Consider the following linear transformation $T:{P}_{2}\to {P}_{3}$, given by $T\left(f\right)=3{x}^{2}f$'. That is, take the first derivative and then multiply by $3{x}^{2}$ (a) Find the matrix for T with respect to the standard bases of ${P}_{n}$: that is, find $\left[T{\right]}_{ϵ}^{ϵ}$, where- $ϵ=1,x,{x}^{2},{x}^{n}$ (b) Find N(T) and R(T). You can either work with polynomials or with their coordinate vectors with respect to the standard basis. Write the answers as spans of polynomials. (c) Find the the matrix for T with respect to the alternate bases: $\left[T{\right]}_{A}^{B}$ where $A=x-1,x,{x}^{2}+1,B={x}^{3},x,{x}^{2},1.$ jernplate8 2020-11-09 Answered

### Prove that by setting these two expressions equal to another, the result is an identity: $d={\mathrm{cos}}^{-1}\left(\mathrm{sin}\left(L{T}_{1}\right)\mathrm{sin}\left(L{T}_{2}\right)+\mathrm{cos}\left(L{T}_{1}\right)\mathrm{cos}\left(L{T}_{2}\right)\mathrm{cos}\left({\mathrm{ln}}_{1}-{\mathrm{ln}}_{2}\right)\right)$ $d=2{\mathrm{sin}}^{-1}\left(\sqrt{{\mathrm{sin}}^{2}\left(\frac{L{T}_{1}-L{T}_{2}}{2}\right)+\mathrm{cos}\left(L{T}_{1}\right)\mathrm{cos}\left(L{T}_{2}\right){\mathrm{sin}}^{2}\left(\frac{{\mathrm{ln}}_{1}-{\mathrm{ln}}_{2}}{2}\right)}\right)$ Braxton Pugh 2020-11-08 Answered

### Whether the statement "I need to be able to graph systems of linear inequalities in order to solve linear programming problems" makes sense or not. banganX 2020-11-08 Answered

### Prove that: If A or B is nonsingular, then AB is similar to BA Ava-May Nelson 2020-11-08 Answered

### The given matrix is the augmented matrix for a system of linear equations. Give the vector form for the general solution. $\left[\begin{array}{cccc}1& 0& -1& -2\\ 0& 1& 2& 3\end{array}\right]$ Trent Carpenter 2020-11-06 Answered

### (i)Prove that if${v}_{1},{v}_{2}$is linearly dependent, then are multiple of each other, that is, there exists a constant c such that . (ii)Prove that the converse of(i) is also true.That is to say, if there exists a constant c such that , 1. then${v}_{1},{v}_{2}$is linearly dependent. Amari Flowers 2020-11-06 Answered

### The line $2x+3y=8$ meets the curve $2{x}^{2}+3{y}^{2}=110$ at the points A and B. Find the coordinates of A and B. Chesley 2020-11-05 Answered

### To graph: The sketch of the solution set of system of nonlinear inequality Kaycee Roche 2020-11-05 Answered

### To determine: Find the sets of points in space whose coordinates satisfy the given combinations of equation and inequalities: a) $y\ge {x}^{2},z\ge 0,$ b) $x\le {y}^{2},0\le z\le 2.$ Maiclubk 2020-11-03 Answered

### Interraption: To show that the system $\stackrel{˙}{r}=r\left(1-{r}^{2}\right),\stackrel{˙}{\theta }=1$ is equivalent to $\stackrel{˙}{x}=x-y-x\left({x}^{2}+{y}^{2}\right),\stackrel{˙}{y}=x+y-y\left({x}^{2}+{y}^{2}\right)$ for polar to Cartesian coordinates. A limit cycle is a closed trajectory. Isolated means that neighboring trajectories are not closed. A limit cycle is said to be unstable or half stable, if all neighboring trajectories approach the lemin cycle. These systems oscillate even in the absence of external periodic force. Joni Kenny 2020-11-03 Answered

### Find the matrix of the linear mapping. $L\left(x,y,z\right)=\left(x+y+z\right)$ cistG 2020-11-02 Answered

### The coefficient matrix for a system of linear differential equations of the form ${y}_{1}=Ay$ has the given eigenvalues and eigenspace bases. Find the general solution for the system ${\lambda }_{1}=3+i⇒\left\{\left[\begin{array}{c}2i\\ i\end{array}\right]\right\},{\lambda }_{2}=3-i⇒\left\{\left[\begin{array}{c}-2i\\ -i\end{array}\right]\right\}$ fortdefruitI 2020-11-02 Answered

### Consider the following two bases for ${R}^{3}$ : If (that is, express x in the $\beta$ coordinates). Jason Farmer 2020-11-01 Answered

### The equivalent polar coordinates for the given rectangular coordinates. A rectangular coordinate is given as (0, -3). CoormaBak9 2020-11-01 Answered

### 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 Answered

### To calculate: The intercepts on the coordinate axes of the straight line with the given equation $2y-4=3x$ e1s2kat26 2020-11-01 Answered

### 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 texelaare 2020-11-01 Answered

### The given matrix is the augmented matrix for a system of linear equations. Give the vector form for the general solution. $\left[\begin{array}{cccccc}1& -1& 0& -2& 0& 0\\ 0& 0& 1& 2& 0& 0\\ 0& 0& 0& 0& 1& 0\end{array}\right]$ Cheyanne Leigh 2020-11-01 Answered

### 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).

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.