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bagirrra123 [75]

2 years ago

11

Fix a matrix A and a vector b. Suppose that y is any solution of the homogeneous system Ax=0 and that z is any solution of the s

ystem Ax=b. Show that y+z is also a solution of the system Ax=b.

1 answer:

ohaa [14]2 years ago

3 0

Answer:

Since y is a solution of the homogeneus system then satisfies Ay=0.

Since z is a solution of the system Ax=b then satisfies Az=b.

Now, we will show that A(y+z)=b.

Observe that A(y+z)=Ay+Az by properties of the product of matrices.

By hypotesis Ay=0 and Az=b.

Then A(y+z)=Ay+Az=0+b=b.

Then A(y+z)=b, this show that y+z is a solution of the system Ax=b.

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By definition, the volume of a cone is given by:
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Rewriting:
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Read 2 more answers

Mike bought five items for lunch that Cost a total of 4.55 .Hit dogs cost .1.10 each and cookies cost 0.75 each. What equation c

-Dominant- [34]

Answer:

$c + h = 5$ and

$0.75c + 1.10h = 4.55$

Step-by-step explanation:

Assume that Mike bought only cookies and hot dogs.

The total can be represented as:

$Cookies + Hot\ Dogs = 5$ --- (1)

And the amount spent can be represented as:

$Cost\ of\ cookies + Cost\ of\ hot\ dogs = 4.55$ --- (2)

Required

Determine the system of equation

Let c represents the number of cookies and h, number of hot dogs.

$Cookies + Hot\ Dogs = 5$ implies $c + h = 5$

And

$Cost\ of\ cookies + Cost\ of\ hot\ dogs = 4.55$

Cost of cookies = 0.75 * c

Cost of hot dogs = 1.10 * h

So, we have:

$0.75c + 1.10h = 4.55$

Hence, the equations are:

$c + h = 5$ and

$0.75c + 1.10h = 4.55$

Solving for c and h

Make c the subject in $c + h = 5$

$c = 5 - h$

Substitute 5 - h for c in $0.75c + 1.10h = 4.55$

$0.75(5- h) + 1.10h = 4.55$

$3.75- 0.75h + 1.10h = 4.55$

$3.75 +0.35h = 4.55$

Collect Like Terms

$0.35h = 4.55 - 3.75$

$0.35h = 0.8$

Solve for h

$h = 0.8/0.35$

$h = 2.28571428571$

$h =2$ -- approximated

Recall that:

$c = 5 - h$

$c = 5 - 2$

$c =3$

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3 years ago