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S_A_V [24]
3 years ago
5

Consider the basis B of R2 consisting of vectors

Mathematics
2 answers:
adelina 88 [10]3 years ago
5 0

The idea is to find a linear combination a_1(5, -6) + a_2(-2, -2) = (-6, 2) It boils down to a system of equations: Take the augmented matrix:

<span>[<span><span>5<span>−6</span></span><span><span>−2</span><span>−2</span></span><span><span>−6</span>2</span></span>]</span> Reduced form: <span>[<span><span>10</span><span>01</span><span><span>−<span>811</span></span><span>1311</span></span></span>]</span> -(8/11)*(5, -6) + (13/11)*(-2, -2) = (-6, 2)

dmitriy555 [2]3 years ago
4 0

Answer:  The required vector x is

x=\begin{bmatrix}-\dfrac{8}{11}\\ \dfrac{13}{11}\end{bmatrix}.

Step-by-step explanation:  Given that a basis B of R² consists of vectors (5, -6) and (-2, -2).

We are to find the vector x in R² whose co-ordinate vector relative to the basis B is \begin{bmatrix}-6\\ 2\end{bmatrix}.

Let us consider that a, b are scalars such that

a(5,-6)+b(-2,-2)=(-6,2)\\\\\Rightarrow (5a-2b,-6a-2b)=(-6,2)\\\\\Rightarrow 5a-2b=-6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-6a-2b=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

Subtracting equation (ii) from equation (i), we get

(5a-2b)-(-6a-2b)=-6-2\\\\\Rightarrow 11a=-8\\\\\Rightarrow a=-\dfrac{8}{11}

and from equation (i), we get

5\times\left(-\dfrac{8}{11}\right)-2b=-6\\\\\\\Rightarrow 2b=-\dfrac{40}{11}+6\\\\\\\Rightarrow 2b=\dfrac{26}{11}\\\\\\\Rightarrow b=\dfrac{13}{11}.

Thus, the required vector x is

x=\begin{bmatrix}-\dfrac{8}{11}\\ \dfrac{13}{11}\end{bmatrix}.

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9. Change the given equation to the form y = mx + b. Give the values of b and m.
rosijanka [135]
X+4y=16
subtract x
4y = -x+16
divide 4 from 4y and divide by 4 on other side too
(4y/4) = (-x/4) + (16/4)

y=-1/4x+4
M=-1/4
B=4
8 0
3 years ago
36. Mrs. Smith will install a ceiling fan in cach room of
otez555 [7]

Answer:

4353.5

Step-by-step explanation:

2 bedrooms and a living room, sorry I forgot to add that in, there's also 3 small windows and a large one

3 rooms

552*3 = 1656

small window = 539.50 * 3 = 1618.50

Large window - 2*539.50 = 1079

1656+1618.5+1079=4353.5

5 0
3 years ago
Find the median and mean of the data set below:<br> 47,15, 6, 49, 45, 30
Georgia [21]

Answer:

The median of the data set:

6, 15, 30, 45, 47, 49

The middle numbers are 30 and 45 so

You have to do 30 + 45

= 75

Then do 75 ÷ 2

= 37.5

The mean of the data set:

47, 15, 6, 49, 45, 30 (add them all)

= 192

Then divide 192 by 6 (because there are 6 numbers)

192 ÷ 6

= 32

So the median is 37.5 and the mean is 32.

Step-by-step explanation:

Hope this helps!

From your neighborhood softie :)

5 0
2 years ago
For what values of m does the graph of y = 3x^2+ 7x + m have two x-intercepts?
qaws [65]

Answer:

m < 49/12

Step-by-step explanation:

The portion of the quadratic formula under the square root sign is the discriminant.

If the discriminant is > 0 then there are two real roots.

b² -4ac > 0

-----------------------------

7² - 4(3)m > 0

49 - 12m > 0

Subtract 49 from both sides

-12m > -49

Divide both sides by -12

(when multiplying or dividing by a negative the inequality must be reversed)

m < 49/12

8 0
3 years ago
2.) Bob has two weekend jobs. Last weekend he made a total of $77 after
Butoxors [25]

Answer:

Step-by-step explanation:

x= money earned per hour working as a cashier.

y=money earned per hour working delivering newspapers.

We propose the following system of equations:

5x + 4y =77

6x + 3y=78

We solve the system by reduction method:

-6*(5x+4y=77) ⇒  -30x-24y=-462

5*(6x+3y=78)⇒     30x+15y=390

                             ---------------------------

                                     -9y=-72  ⇒   y=-72 /-9=8

Now, we get the value of "x" replacing the value of "y" by "8" in any part of the equation above.

5x + 4(8)=77

5x+32=77

5x=77-32

5x=45

x=45/5=9

therefore;  

money earned per hour working as a cashier= $9/ hour

money earned per hour working delivering newspapers=$8/hour

7 0
3 years ago
Read 2 more answers
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