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Nataly [62]
3 years ago
11

Simplify: −7 + {12 − 3[50 − 4(2 + 3) ] }

Mathematics
1 answer:
DedPeter [7]3 years ago
6 0

Answer:

-85

Step-by-step explanation:

<em><u>1) (2 + 3)</u></em>

-7 + {12 - 3[50 - 4(5) ] }

<em><u>2) -7 + {12 - 3[50 - 20] }</u></em>

-7 + {12 - 3[30] }

<em><u>3) -7 + 12 - 90</u></em>

5 - 90

<u>Answer: -85</u>

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Suppose that v is an eigenvector of matrix A with eigenvalue λA, and it is also an eigenvector of matrix B with eigenvalue λB. (
galben [10]

Answer:

(a) Yes, λ_{A}+λ_{B}

(b) Yes, λ_{A}λ_{B}

Step-by-step explanation:

First, lets understand what are eigenvectors and eigenvalues?

Note: I am using the notation λ_{A} to denote Lambda(A) sign.

v is an eigenvector of matrix A with eigenvalue λ_{A}

v is also eigenvector of matrix B with eigenvalue λ_{B}

So we can write this in equation form as

Av=λ_{A}v

So what does this equation say?

When you multiply any vector by A they do change their direction. any vector  that is in the same direction as of Av, then this v  is called the eigenvector of A. Av is λ_{A} times the original v. The number λ_{A} is the eigenvalue of A.

λ_{A} this number is very important and tells us what is happening when we multiply Av. Is it shrinking or expanding or reversed or something else?

It tells us everything we need to know!

Bonus:

By the way you can find out the eigenvalue of Av by using the following equation:

det(A-λI)=0

where I is identity matrix of the size of same as A.

Now lets come to the solution!

(a) Show that v is an eigenvector of A + B and find its associated eigenvalue.

The eigenvalues of A and B are λ_{A} and λ_{B}, then

(A+B)(v)=Av+Bv=(λ_{A})v + (λ_{B})v=(λ_{A}+λ_{B})(v)

so,  (A+B)(v)=(λ_{A}+λ_{B})(v)

which means that v is also an eigenvector of A+B and the associated eigenvalues are λ_{A}+λ_{B}

(b) Show that v is an eigenvector of AB and find its associated eigenvalue.

The eigenvalues of A and B are λ_{A} and λ_{B}, then

(AB)(v)=A(Bv)=A(λ_{B})=λ_{B}(Av)=λ_{B}λ_{A}(v)=λ_{A}λ_{B}(v)

so,  

(AB)(v)=λ_{A}λ_{B}(v)

which means that v is also an eigenvector of AB and the associated eigenvalues are λ_{A}λ_{B}

5 0
3 years ago
Dersan went for a run to prepare for a long distance race coming up. From his house, he ran 6 miles directly north, and then 8 m
ella [17]

Answer:

24

Step-by-step explanation:

So, Dersan's path is a right triangle. You have to find the last side. You can use the triples or 6^2+8^2=c^2 but I'll use a triple.

3,4,5.

The last side is 10.

6+8+10=24

hope this helped!

3 0
2 years ago
Which is the solution to the equation 8.25 + 1/4 W = 10.75? Round to the nearest hundredth if necessary.
murzikaleks [220]
8.25+\dfrac{1}{4}w=10.75\ \ \ \ |-8.25\\\\\dfrac{1}{4}w=2.5\ \ \ |\cdot4\\\\w=10
3 0
3 years ago
Please help will give brainlest
shtirl [24]

Answer:

18

Step-by-step explanation:

Here,

given,

a=3 and b=6

Then

4a+b=?

Put respective values on 4a+b

4*3+6

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6 0
1 year ago
Read 2 more answers
HELP! I am confused since the -5 was added, so would it be the slope or would -7 be the slope?
In-s [12.5K]

Answer:

slope = 35; y-intercept = -45

Step-by-step explanation:

Function f(x) is written in the slope-intercept form, y = mx + b.

f(x) = -7x + 9

You compare it with

f(x) = mx + b, and you see that m, the slope, is -7, and b, the y-intercept is 9.

Now we deal with function h(x).

h(x) = -5(-7x + 9)

This is not written in the y = mx + b form, but we can put it in that form by distributing the -5.

h(x) = 35x - 45

Now, h(x) is written in the y = mx + b form. We see clearly that m = 35, so the slope of function h is 35. We also see that b, the y-intercept is -45.

Answer: slope = 35; y-intercept = -45

5 0
3 years ago
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