# Linear algebra questions and answers

Recent questions in Linear algebra
Lennie Carroll 2020-10-28 Answered

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

tricotasu 2020-10-26 Answered

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

CoormaBak9 2020-10-25 Answered

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

Jason Farmer 2020-10-21 Answered

### 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.

necessaryh 2020-10-21 Answered

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

waigaK 2020-10-21 Answered

### Consider the following vectors in $$\displaystyle{R}^{{4}}:$$ $$v_1 = \begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \end{bmatrix}, v_2 = \begin{bmatrix} 0 \\ 1 \\ 1 \\ 1 \end{bmatrix} v_3 = \begin{bmatrix}0 \\ 0 \\ 1 \\ 1 \end{bmatrix}, v_4 = \begin{bmatrix} 0 \\ 0 \\ 0 \\ 1 \end{bmatrix}$$ d. If $$x = \begin{bmatrix} 23 \\ 12 \\ 10 \\ 19 \end{bmatrix}, find \left\{ x\right\}_B e$$. If $${x}_B = \begin{bmatrix} 3 \\ 1 \\ -4 \\ -4 \end{bmatrix}$$, find x.

Brennan Flores 2020-10-21 Answered

### 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 $$\displaystyle{90}^{{\circ}}$$. u = (-1, -1, 8, 0), v = (5,6,1,4)

Lennie Carroll 2020-10-20 Answered

### Consider the linear transformation $$\displaystyle{U}:{R}^{{3}}\rightarrow{R}^{{3}}$$ 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 $$\epsilon = \left\{ \left(\begin{array}{c}1\\ 0 \\0\end{array}\right), \left(\begin{array}{c}0\\ 1 \\ 0\end{array}\right), \left(\begin{array}{c}0\\ 0 \\ 1\end{array}\right) \right\}, \gamma = \left\{ \left(\begin{array}{c}1 - i\\ 1 + i \\ 1 \end{array}\right), \left(\begin{array}{c} -1\\ 1 \\ 0\end{array}\right), \left(\begin{array}{c}0\\ 0 \\ 1\end{array}\right) \right\}$$, Compute the four coordinate matrices $$\displaystyle{{\left[{U}\right]}_{{\epsilon}}^{{\gamma}}},{{\left[{U}\right]}_{{\gamma}}^{{\gamma}}},$$

tinfoQ 2020-10-18 Answered

### 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 Answered

### 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 $$\displaystyle{B}_{{1}}\to{B}_{{2}}$$ and next use this matrix to covert the coordinate vector $$\overrightarrow{v}_{B_1} = \left(\begin{array}{c}2\\ -1\end{array}\right)$$ of v to its coodirnate vector $$\overrightarrow{v}_{B_2}$$

Wribreeminsl 2020-10-18 Answered

### Given the elow bases for $$R^2$$ and the point at the specified coordinate in the standard basis as below, (40 points) $$(B1 = \left\{ (1, 0), (0, 1) \right\}$$& $$B2 = (1, 2), (2, -1) \}$$(1, 7) = $$3^* (1, 2) - (2, 1)$$ $$B2 = (1, 1), (-1, 1) (3, 7 = 5^* (1, 1) + 2^* (-1,1)$$ $$B2 = (1, 2), (2, 1) \ \ \ (0, 3) = 2^* (1, 2) -2^* (2, 1)$$ $$(8,10) = 4^* (1, 2) + 2^* (2, 1)$$ 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.
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