Denote the unit vectors of R^3 by $e_1=(1,0,0), e_2=(0,1,0), e_3=(0,0,1)$ . Now consider $v_1=e_1, v_2=2e_1$ and $v_3=e_3$ . We have that $v_1, v_2,v_3 \in \mathbb{R}^3$ . Also, the vector $v_3$ is not a linear combination of $v_1, v_2$ because any linear combination of these two vectors will have third coordinate zero, but v_3 has third coordinate 1 so they can't be equal.

However, the set $\{v_1, v_2,v_3\}$ is not linearly independent, because $2v_1-v_2+0v_3=0$ is a non-trivial linear combination of these vectors that equals zero.

4 0

3 years ago

PLEASE HELP ME!!!!!!!!!!!!!!!!!!

liberstina [14]

I think the answer is ;B.316 and 38

8 0

2 years ago

Read 2 more answers

There exists a linear function f(x) such that f(6) = 8, f(2)=20, and f(a) = 16. What is the value of 2a?

atroni [7]

Answer:

a = 10/3.

Step-by-step explanation:

We write the linear function as follows:

f(x) = mx + b where m is the slope and b is the y-intercept.

f(6) = 6m + b = 8

f(2) = 2m + b = 20 Subtracting these 2 equations:

4m = -12

m = -3.

and -3 * 2 + b = 20 so:

b = 20 + 6 = 26.

So we have the linear function:

f(x) = -3 x + 26

f(a) = 16 = -3 a + 26

-3 a = 16-26

a = -10 * -3 = 10/3.

3 0

2 years ago

9. A rectangular shoebox is 14 inches long by 8 inches wide by 6 inches tall.

andreyandreev [35.5K]

Answer:

J 672 cubic inches

Step-by-step explanation:

The volume of a rectangular prism is

V = l*w*h

V = 14 inches * 8 inches * 6 inches

V =672 inches^3

3 0

2 years ago