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

10 + 2n = 8n - 2n + 10

galina1969 [7]

Answer:

n=0

Step-by-step explanation:

Rearrange

10+2=8−2+10

2+10=8−2+10

Combine like terms

2n+10=8n−2n+10

2+10=6+10

Subtract from both sides

2+10=6+10

2+10−10=6+10−10

Simplify

2n=6n

Subtract both sides from 6n of the equation

2=6

2−6=6−6

Solution

n=0

5 0

2 years ago

What is the five-number summary for this data set?

Free_Kalibri [48]

Answer:

Step-by-step explanation:

min and max are correctly the same for all 4 answers.

we have 10 data points, so, the median is the mean value between the 2 middle numbers, 19 and 22 : 20.5.

ah, it can be only C or D.

Q1 is the median of the lower half of data points (13 out of 11, 12, 13, 17, 19). and Q3 is the median of the upper half of data points (29 out of 22, 24, 29, 33, 38).

so, C is correct.

7 0

1 year ago

Please can someone help?

Alina [70]

Step-by-step explanation:

R = 6.5cm and r = 2.3 cm

area of the shaded region = area of the outer circle - area of the inner circle

= πR²-πr²

=π(R²-r²)

=π{(6.5)²-(2.3)²}

=π (42.25-5.29)

= 3.14× 36.96

= 115.866

= 116 cm²

6 0

3 years ago