 # Linear algebra questions and answers

Recent questions in Linear algebra elbluffz1 2022-01-29 Answered

### Given the linear transformation: $T\left(M\right)=\left[\begin{array}{cc}1& 0\\ 0& 2\end{array}\right]M-M\left[\begin{array}{cc}1& 0\\ 0& 2\end{array}\right]$ a) Find the matrix B of T w respect to the standard basis B of ${\mathbb{R}}^{2×2}$. b) Find bases of the image and kernel of B? Cassarrim1 2022-01-29 Answered

### Let $e=\left(a,b,c\right)$ be a unit vector in ${\mathbb{R}}^{3}$ and let T be the linear transformation on ${\mathbb{R}}^{3}$ of rotation by ${180}^{\circ }$ about e. Find the matrix for T with respect to the standard basis and ${e}_{3}=\left(0,0,1\right)$. The rotation matrix in ${\mathbb{R}}^{3}$ by ${180}^{\circ }$ is : $\left[\begin{array}{ccc}-1& 0& 0\\ 0& -1& 0\\ 0& 0& 1\end{array}\right]$ So rotating e by ${180}^{\circ }$ gives : $\left[\begin{array}{c}-a\\ -b\\ c\end{array}\right]$ After that how to get the transformation matrix w.r.t the standard basis? Emmy Combs 2022-01-29 Answered

### Matrix transformation $f:{\mathbb{R}}^{3}\to {\mathbb{R}}^{3}$ $\left(\begin{array}{ccc}4& 1& 3\\ 2& -1& 3\\ 2& 2& 0\end{array}\right)$ Establish x,y and z such that, $f\left(\begin{array}{c}x\\ y\\ z\end{array}\right)$ Do I just need to multiply the values of f for the $3×3$ matrix? What does this mean overall? FiessyFrimatsd0 2022-01-29 Answered

### Find the basis for kernel of a matrix transformation Let $\psi :\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)\to \left(\begin{array}{cc}a+b& a-c\\ a+c& b-c\end{array}\right)$ Find basis for ker $\psi$ Reese Munoz 2022-01-29 Answered

### # A local university football team has ordera national power to next yerar’s schedule.the order team has agreed to play the game guaranteed fee of $100000 .plus 25 percent of the gate receipts .assume the ticket price is$ 12 . (a) determine the number od tickets which must be sold to recover the $100000 guarantee. (b) if college official hope to net a profit of$2400000 from the game how many tickets must be sold .(c) if a sellout of 50000 fans is assured , what ticket price would allow the university to earn the desired profit of $240000. ( d) assuming a total sell out , what would total profit equal if the the$ 12price is charged.​ Branden Valentine 2022-01-24 Answered

### What are the standard three-dimensional unit vectors? m4tx45w 2022-01-24 Answered

### Suppose there was a basis for and a certain number of dimensions for subspace W in ${\mathbb{R}}^{4}$.Why is the number of dimensions 2? $W=\left\{⟨4s-t,s,t,s⟩\mid s,t\in \mathbb{R}\right\}$ For instance, apparently, $\left\{⟨0,1,4,1⟩,⟨1,1,3,1⟩\right\}$ is a valid set, and it happens to be of dimension 2 in ${\mathbb{R}}^{4}$. Does a basis for ${\mathbb{R}}^{n}$ have to have n vectors? David Rojas 2022-01-24 Answered

### Let $V={\mathbb{R}}^{3}$ and $W=\left\{\left(x,y,z\right)\mid x,y,z\in \mathbb{Q}\right\}$. Is $W\le V$? Justify your answer.So, I wrote:1) $\left(0,0,0\right)\in W$2) $\alpha ,\beta \in W$$\alpha =\left(x,y,z\right),\beta =\left({x}^{\prime },{y}^{\prime },{z}^{\prime }\right)$$\alpha ,\beta =\left(x+{x}^{\prime },y+{y}^{\prime },z+{z}^{\prime }$ so $\alpha +\beta \in W$3) $c\in \mathbb{R},\alpha \in W$$\alpha =\left(x,y,z\right)$$c\alpha =\left(cx,cy,cz\right)$ so $c\alpha \in W$Hence, $W\le V$ maliaseth0 2022-01-24 Answered

### How could I determine whether vectors $P<-2,7,4>,Q<-4,8,1>,\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}R<0,6,7>$ are all in the same plane? licencegpopc 2022-01-24 Answered

### Let $V=Span\left\{{f}_{1},{f}_{2},{f}_{3}\right\}$, where ${f}_{1}=1,{f}_{2}={e}^{x},{f}_{3}=x{e}^{x}$ a) Prove that $S=\left\{{f}_{1},{f}_{2},{f}_{3}\right\}$ is a basis of V. b) Find the coordinates of $g=3+\left(1+2x\right){e}^{x}$ with respect to S. c) Is $\left\{{f}_{1},{f}_{2},{f}_{3}\right\}$ linearly independent? jelentetvq 2022-01-24 Answered

### How do I find the unit vector for $v=<2,-5,6>$ maliaseth0 2022-01-24 Answered

### What is the magnitude of vector $AB$ if $A=\left(4,2,-6\right)$ and $B=\left(9,-1,3\right)$? Lainey Goodwin 2022-01-24 Answered

### Geometrically, the span of two non-parallel vectors in ${R}^{3}$ is? 1) one octant 2) a line 3) a point 4) the whole 3-space 5) a plane jelentetvq 2022-01-24 Answered

### Let $\stackrel{\to }{{v}_{1}}=\left[\begin{array}{c}2\\ 3\end{array}\right]$ and $\stackrel{\to }{{v}_{1}}=\left[\begin{array}{c}4\\ 6\end{array}\right]$ what is the **span** of the vector space defined by $\stackrel{\to }{{v}_{1}}$ and $\stackrel{\to }{{v}_{1}}$? Explain your answer in detail? shangokm 2022-01-24 Answered

### Prove that in a real vector space $V\cdot c\left({}^{\prime }\alpha -\beta \right)=c\cdot \alpha -c\cdot \beta$where $c\in \mathbb{R};\alpha ,\beta \in V$? elbluffz1 2022-01-24 Answered

### Let say K and L are two different subspace real vector space V. If given $\mathrm{dim}\left(K\right)=\mathrm{dim}\left(L\right)=4$, how to determine minimal dimensions are possible for V? Anika Klein 2022-01-23 Answered

### Solve the system by inverting the coefficient matrix ${x}_{1}+3{x}_{2}+{x}_{3}=4$ $2{x}_{1}+2{x}_{2}+{x}_{3}=-1$ $2{x}_{1}+3{x}_{2}+{x}_{3}=3$ trefoniu1 2022-01-23 Answered

### Linear transformation has unique standard matrx? $\left[T\right]=-I$

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.