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Determine if b is a linear combination of a1 a2, and a3. a1 = [ 1 -2 0 ], a2 = [ 0 1 3 ], a3 = [ 6 -6 18 ], b = [ 2 -2 6 ] Choos

marysya [2.9K]

Answer: Vector b is not a linear combination

Step-by-step explanation:

First of all we put the vectors in terms of different variables, such as:

a1(1,-2,0)=(a,-2a,0);

a2(0,1,3)=(0,b,3b);

a3(6,-6,18)=(6c,-6c,18c);

To know that a vector is a linear combination we need to express it like a sum of other different vectors.

(2,-2,6)=(a,-2a,0)+(0,b,3b)+(6c,-6c,18c)

(2,-2,6)=(a+0+6c,-2a+b-6c,0+3b+18c)

We express this sum like a system of equations.

a+6c=2

-2a+b-6c=-2

3b+18c=6

We solve this system of equations and we can note that the system don't have a solution, so the vector b is not a linear combination of a1, a2, and a3.

8 0

3 years ago

Read 2 more answers

Help me, I will appreciate it

AveGali [126]

They are corresponding angles - they are equal
X+95 =4x-10
Add 10 to both sides
X+105 =4x
Subtract x from both sides
105=3x
X=35

35+95= 130

7 0

3 years ago

Tim looks up at the top of a tree at an angle of elevation of 40 degrees. If heis 5 ft tall and 10 ft from the tree, how tall is

dolphi86 [110]

<h2>Answer:</h2>

13.391 ft

<h2>Explanations:</h2>

The schematic diagram of the given question is shown below;

The height of the tree is expressed as:

H = h +5

Determine the value of h using the SOH CAH TOA identity

$\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ tan40^0=\frac{h}{10} \\ h=10tan40 \\ h=10(0.8391) \\ h=8.391ft \\ \end{gathered}$

Determine the height of the tree

$\begin{gathered} H=h+5 \\ H=8.391+5 \\ H=13.391ft \end{gathered}$

Hence the height of the tree is 13.391ft

3 0

1 year ago

the wireless cafe charges $5.40 for 45 minutes of internet access. how much money doe the wireless cafe charge per minute

ki77a [65]

5.40 divided by 45 = 0.12

The cafe charges 12 cents per minute.

8 0

4 years ago

3/4 over 3 1/4 simplified is?

Sergio039 [100]

Answer:

Convert

3

1

4

to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

3

+

1

4

−

1

3

4

Add

3

and

1

4

To write

3

as a fraction with a common denominator, multiply by

4

.

3

⋅

4

+

1

4

−

1

3

4

Combine

3

and

4

.

3

⋅

4

+

1

4

−

1

3

4

Combine the numerators over the common denominator.

3

⋅

4

+

1

4

−

1

3

4

Simplify the numerator.

Multiply

3

by

4

.

12

+

1

4

−

1

3

4

Add

12

and

1

.

13

4

−

1

3

4

Convert

1

3

4

to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

13

4

−

(

1

+

3

4

)

Add

1

and

3

4

.

13

4

−

7

4

Combine the numerators over the common denominator.

13

−

7

4

Subtract

7

from

13

.

6

4

Cancel the common factor of

6

and

4

.

Factor

2

out of

6

.

2

(

3

)

4

Cancel the common factors.

Factor

2

out of

4

.

2

⋅

3

2

⋅

2

Cancel the common factor.

2

⋅

3

2

⋅

2

Rewrite the expression.

3

2

The result can be shown in multiple forms.

Exact Form:

3

2

Decimal Form:

1.5

Mixed Number Form:

1

2

Step-by-step explanation:

6 0

3 years ago