Viktor Wiley

Answered 2021-09-21
Author has **18607** answers

asked 2021-09-27

asked 2021-05-27

Let vectors \(A=(1,0,-3), B =(-2,5,1),\ and\ C =(3,1,1)\). Calculate the following, expressing your answers as ordered triples (three comma-separated numbers).

(C) \((2\bar B)(3\bar C)\)

(D) \((\bar B)(\bar C)\)

(E) \(\overrightarrow A(\overrightarrow B \times \overrightarrow C)\)

(F)If \(\bar v_1 \text{ and } \bar v_2\) are perpendicular, \(|\bar v_1 \times \bar v_2|\)

(G) If \(\bar v_1 \text{ and } \bar v_2\) are parallel, \(|\bar v_1 \times \bar v_2|\)

asked 2022-01-07

Let u and v be distinct vectors of a vector space V. Show that if {u, v} is a basis for V and a and b are nonzero scalars, then both {u+v, au} and {au, bv} are also bases for V.

asked 2021-12-03

Let W be the set of all vectors of the form shown, where a, b, and c represent arbitrary real numbers. In each case, either find a set S of vectors that spans W or give an example to show that W is not a vector space.

\[\begin{bmatrix}4a+3b \\ 0 \\ a+b+c \\ c-2a \end{bmatrix}\]

\[\begin{bmatrix}4a+3b \\ 0 \\ a+b+c \\ c-2a \end{bmatrix}\]

asked 2021-09-25

\(a=(2,3,0), b=(1,0,5)\)

asked 2021-06-03

Let vectors \(\bar{A} =(2,1,-4), \bar{B} =(-3,0,1), \text{ and } \bar{C} =(-1,-1,2)\)

Calculate the following:

A)\(\bar{A} \cdot \bar{B}\)?

E)Which of the following can be computed?

\(\bar{A} \cdot \bar{B} \cdot \bar{C}\)

\(\bar{A}(\bar{B} \cdot \bar{C})\)

\(\bar{A}(\bar{B} + \bar{C})\)

\(3\bar{A}\)

F)Express your answer in terms of \(v_1\)

G) If \(v_1 \text{ and } v_2\) are perpendicular?

H) If \(v_1 \text{ and } v_2\) are parallel?

Calculate the following:

A)\(\bar{A} \cdot \bar{B}\)?

E)Which of the following can be computed?

\(\bar{A} \cdot \bar{B} \cdot \bar{C}\)

\(\bar{A}(\bar{B} \cdot \bar{C})\)

\(\bar{A}(\bar{B} + \bar{C})\)

\(3\bar{A}\)

F)Express your answer in terms of \(v_1\)

G) If \(v_1 \text{ and } v_2\) are perpendicular?

H) If \(v_1 \text{ and } v_2\) are parallel?

asked 2021-09-19

v is a set of ordered pairs (a, b) of real numbers. Sum and scalar multiplication are defined by: (a, b) + (c, d) = (a + c, b + d)
k (a, b) = (kb, ka) (attention in this part)
show that V is not linear space.