#### Didn’t find what you are looking for?

Vectors and spaces

### Let $$\displaystyle{A}={b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{a}&{b}\backslash{c}&{d}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}$$ and 'k' be the scalar. Find the formula that relates 'detKA' to 'K' and 'detA''

Vectors and spaces

### Let the vector space $$P^{2}$$ have the inner product $$\langle p,q\rangle=\int_{-1}^{1} p(x)q(x)dx.$$ Find the following for $$p = 1\ and\ q = x^{2}.$$ $$(a) ⟨p,q⟩ (b) ∥p∥ (c) ∥q∥ (d) d(p,q)$$

Vectors and spaces

### Find all scalars $$c_{1} , c_{2}, c_{3}$$ such that $$c_{1}(1 , -1, 0) + c_{2}(4, 5, 1) + c_{3}(0, 1, 5) = (3, 2, -19)$$

Vectors and spaces

### The position vector $$\displaystyle{r}{\left({t}\right)}={\left\langle{n}{t},\frac{{1}}{{t}^{{2}}},{t}^{{4}}\right\rangle}$$ describes the path of an object moving in space. (a) Find the velocity vector, speed, and acceleration vector of the object. (b) Evaluate the velocity vector and acceleration vector of the object at the given value of $$\displaystyle{t}=\sqrt{{3}}$$

Vectors and spaces

### A city planner wanted to place the new town library at site A. The mayor thought that it would be better at site B. What transformations were applied to the building at site A to relocate the building to site B? Did the mayor change the size or orientation of the library? [Pic]

Vectors and spaces

### Use $$\displaystyle{A}{B}←→$$ and $$\displaystyle{C}{D}←→$$ to answer the question. $$\displaystyle{A}{B}←→$$ contains the points A(2,1) and B(3,4). $$\displaystyle{C}{D}←→$$ contains the points C(−2,−1) and D(1,−2). Is $$\displaystyle{A}{B}←→$$ perpendicular to $$\displaystyle{C}{D}←→$$? Why or why not?

Vectors and spaces

### Let u,v1 and v2 be vectors in R^3, and let c1 and c2 be scalars. If u is orthogonal to both v1 and v2, prove that u is orthogonal to the vector c1v1+c2v2.

Vectors and spaces

### Let U,V be subspaces of Rn. Suppose that U⊥V. Prove that {u,v} is linearly independent for any nonzero vectors u∈U,v∈V.

Vectors and spaces

### Write an equation of the line that passes through (3, 1) and (0, 10)

Vectors and spaces

### Let U and W be vector spaces over a field K. Let V be the set of ordered pairs (u,w) where u ∈ U and w ∈ W. Show that V is a vector space over K with addition in V and scalar multiplication on V defined by (u,w)+(u',w')=(u+u',w+w') and k(u,w)=(ku,kw) (This space V is called the external direct product of U and W.)

Vectors and spaces

### What is the slope of EF if E is (0,-2) and F is (3, 2.5)

Vectors and spaces

### Determine if $$\displaystyle{a}.{H}={\left\lbrace\frac{{{x},{y}}}{{y}}={3}{x}-{1}\right\rbrace}$$ is a subspace of R2 $$\displaystyle{b}.{H}={\left\lbrace{a}{t}+\frac{{b}}{{b}}={8}{a}\right\rbrace}$$ is a subspace of P1

Vectors and spaces

### m Find m Y=(6x+44) Z=(-10x+65)

Vectors and spaces

### Find the distance UV between the points U(7,−4) and V(−3,−6). Round your answer to the nearest tenth, if neces

Vectors and spaces

### Determine the area under the standard normal curve that lies between ​ (a) Upper Z equals -2.03 and Upper Z equals 2.03​, ​(b) Upper Z equals -1.56 and Upper Z equals 0​, and ​(c) Upper Z equals -1.51 and Upper Z equals 0.68. ​ ​(Round to four decimal places as​ needed.)

Vectors and spaces

### A vector is first rotated by $$\displaystyle{90}^{\circ}$$ along x-axis and then scaled up by 5 times is equal to $$\displaystyle{\left({15},-{10},{20}\right)}$$. What was the original vector

Vectors and spaces

### Suppose the vertices of the original figure in the example were A(-6,6), B(-2,5), and C(-6,2). What would be the vertices of the image after a 90° clockwise rotation about the origin? A'() B'() C'(___)

Vectors and spaces