# Questions and Answers

# Your Questions About X1

Helen asks…

## How do i find the conditions so that the following linear system is consistent?

Find conditions on a,b and c so that the following system is consistent :

**x1**+x2+2×3 = a

**x1**+x3 = b

2×1 + x2+3×3 = c

In particular if a = 1 and b = 2, find the value for c that makes the linear system consistent.

### Administrator answers:

(1) x1 + x2+2×3 = a

(2) x1 + 0×2 +x3 = b

(3) 2×1 + x2+3×3 = c

——————— subtract (1)-(2)

X2 + x3 = a-b

———————subtract 2(1) -(3)

X2 + x3 = 2a-c

Example: at this point , If x2 + x3 = 7 and x2+ x3 = 9

We would get 7= 9, which means no solution, and inconsistent.

So a-b = 2a -c

Or

a+ b= c

So if a= 1 and b= 2, then c must equal 1+2= 3

I hope this helps!

Susan asks…

## What portable laptop would you recommend for school use?

I am graphic design student, so my main use for this is mostly adobe CS6; and I also do a bit of video editing.

I am leaning towards purchasing an ultrabook, more specifically, the Lenovo Thinkpad **X1** Carbon.

Any other laptops I should consider purchasing?

I have considered Macbooks, but I figure,I can purchase a windows laptop with the same specs for a little cheaper.

### Administrator answers:

You really can’t go wrong with Macs for design. If you are absolutely bent on going with a Windows laptop, get something with an i7 Intel chip, third generation. The Lenovo Thinkpad X1 Carbon looks like it will work. But, I got my macbook for much less than what Carbon is retailing for. If you’re freelancing in graphic design, check out http://freelancegraphicdesigner.info/ as a resource! Best of luck!

Richard asks…

## How to do describe a general body translation and rotation?

How do you describe a rotation and translation of a rigid body in 3 dimensional space?

Say the “center” of the body has location (xo,yo,zo) with respect to the origin. Also say vector (**x1**,y1,z1) extends from the center of the body and is fixed with respect to the body.

### Administrator answers:

The simplest way is to give the velocity of the center of rotation, and the angular velocity around 3 axises of rotation (x,y,z for example with the center of rotation as the origin).

Carol asks…

## How do I calculate the equation of GR2 when I know the solutions?

How do I calculate the equation of gr2 when I know the solutions?

Solutions **x1** and x2

x_1+x_2=2 and x_1x_2=-3

how to calculate with x^2-Sx+P=0 ?

### Administrator answers:

This question is confusing. First, what is GR2 supposed to mean? Second, you don’t calculate equations, you calculate expressions, and solve equations. Third, you don’t say how x? And x? Relate to the quadratic equation x² ? Sx + P = 0.

It’s always best to post the whole question as originally written.

Anyway, I assume that x? And x? Are roots of quadratic equation x² ? Sx + P = 0

and we need to find values of S and P ??

——————————————————————————————

In general: Let x? And x? Be roots of quadratic equation ax²+ bx + c = 0. Then

x? + x? = ?b/a

x? * x? = c/a

Quadratic equation: x² ? Sx + P = 0

x? + x? = ?b/a

2 = S/1

S = 2

x? * x? = c/a

?3 = P/1

P = ?3

x? + x? (as defined above) are roots of quadratic equation: x² ? 2x ? 3 = 0

Joseph asks…

## How to find a matrix of orthogonal projection?

Given the plane **x1** + 2×2 – x3 = 0, how do you find the matrix of orthogonal projection onto this plane in R^3.

### Administrator answers:

Http://lmgtfy.com/?q=matrix+orthogonal+projection

First hit – http://en.wikipedia.org/wiki/Projection_%28linear_algebra%29

Work the rest out for yourself, lazy. Do your own homework.

How will you pass the exam if you get the answers from YA?

Mandy asks…

## Would the babies look identical if two sets of identical twins mated with one another?

Would the babies look identical if two sets of identical twins mated with one another?

So we got Y1 and Y2 and **X1** and X2

**X1** and Y1 got together and make baby A2 and X2 and Y2 go together and make baby A1

Does baby A1 and A2 look identical? If not, is there a chance that they could look identical?

@Dustan

I get it.

### Administrator answers:

No. Do brothers and sisters look identical? No. Even though siblings have very similar DNA they are still different on a genetic and appearance level. This is due to which SPECIFIC genes a sibling gets from its parents.

In your example the Identical brothers mate with Identical sisters. Their children would be equivalent to genetic siblings. However BabyA1 received a different combination of genes from his parents than BabyA2. This combination is essentially random and that is why brothers and sisters look similar, but under most circumstances they do NOT look identical.

Did you know the Mark-Kate and Ashley Olsen are not identical twins? On a genetic level they are Fraternal. Random chance is why they look identical.

Chris asks…

## How do you put two points from a line into standard form?

I never really understood this! >.<

Here are my points (-5,-8) and (5,3)

To I get the slope from them first by doing the y2-y1 over x2-**x1** ?

Or do the point slope formula? Please help!!!

### Administrator answers:

Point 1 = (-5,-8)

Point 2 = (5,3)

y = mx + b

m = (y2 – y1) / (x2 – x1)

In your case y2 = 3, y1 = -8, x2 = 5, x1 = -5

substitute

m = (3 + / (5 + 5) = 11/10

b = y – mx, thus

b = -5/2

this means that your line is (y = mx + b)

y = 11x/10 – 5/2

multiply everything times 10

10y = 11x – 25

rearrange into standard form

11x – 10y = 25 <<< done!

I suggest you see this video on straight lines http://youtu.be/m2hi3TB3m7U

and use this calculator http://matrixlab-examples.com/equation-of-a-straight-line.html

.

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