solve linear equation system

To solve a linear equations system:

x+y+z=3
2x+2y+z=5
4x+8y-3z=9

linsolve is the function to use.

a=[1 1 1; 2 2 1; 4 8 -3];
b=[3;5;9];
linsolve(a,b)

Done!

roots function and solve functioin

Today I learned two methods to solve polynomial.Two functions, roots and solve can be used. For example, if I would like to solve the polynomial:

x^3+2*x^2-8*x+10=0

I can use:

r=roots([1 2 -8 10])

or:

solve('x^3+2*x^2-8*x+10')

However, the answers will be given in different form. The first one will give numerical values of the roots, like:

ans =

  -4.3605          

   1.1803 + 0.9488i

   1.1803 - 0.9488i

the latter one will give symbolic form answers:

ans =

 

-1/3*(215+3*2697^(1/2))^(1/3)-28/3/(215+3*2697^(1/2))^(1/3)-2/3

 1/6*(215+3*2697^(1/2))^(1/3)+14/3/(215+3*2697^(1/2))^(1/3)-2/3+1/2*i*3^(1/2)*(-1/3*(215+3*2697^(1/2))^(1/3)+28/3/(215+3*2697^(1/2))^(1/3))

 1/6*(215+3*2697^(1/2))^(1/3)+14/3/(215+3*2697^(1/2))^(1/3)-2/3-1/2*i*3^(1/2)*(-1/3*(215+3*2697^(1/2))^(1/3)+28/3/(215+3*2697^(1/2))^(1/3))

 

 

I was using a lot of greek symbols in my Word document, and usually when I need one, I input a English letter, for example, "a", then highlight it and change the font to symbol. That way, I will have a "α" there. However, if someone changed the font of that letter, it won't show up correctly- a blank will be left there instead of the letter you want.

I did some research and found one way to solve this problem: Firstly type in the unicode for the greek letter, then press "Alt+X". The unicode will be turned into a greek letter, and changing the font will not cause any trouble. The greek letter will show up anyway, just look a little different when different font is used.

And here is the reference for the unicode. This is very cool!

0391 Α  GREEK CAPITAL LETTER ALPHA

0392 Β  GREEK CAPITAL LETTER BETA

0393 Γ  GREEK CAPITAL LETTER GAMMA

0394 Δ  GREEK CAPITAL LETTER DELTA

0395 Ε  GREEK CAPITAL LETTER EPSILON

0396 Ζ  GREEK CAPITAL LETTER ZETA

0397 Η  GREEK CAPITAL LETTER ETA

0398 Θ  GREEK CAPITAL LETTER THETA

0399 Ι  GREEK CAPITAL LETTER IOTA

039A Κ  GREEK CAPITAL LETTER KAPPA

039B Λ  GREEK CAPITAL LETTER LAMDA

039C Μ  GREEK CAPITAL LETTER MU

039D Ν  GREEK CAPITAL LETTER NU

039E Ξ  GREEK CAPITAL LETTER XI

039F Ο  GREEK CAPITAL LETTER OMICRON

03A0 Π  GREEK CAPITAL LETTER PI

03A1 Ρ  GREEK CAPITAL LETTER RHO

03A3 Σ  GREEK CAPITAL LETTER SIGMA

03A4 Τ  GREEK CAPITAL LETTER TAU

03A5 Υ  GREEK CAPITAL LETTER UPSILON

03A6 Φ  GREEK CAPITAL LETTER PHI

03A7 Χ  GREEK CAPITAL LETTER CHI

03A8 Ψ  GREEK CAPITAL LETTER PSI

03A9 Ω  GREEK CAPITAL LETTER OMEGA

03AA Ϊ  GREEK CAPITAL LETTER IOTA WITH DIALYTIKA

03AB Ϋ  GREEK CAPITAL LETTER UPSILON WITH DIALYTIKA

03B1 α  GREEK SMALL LETTER ALPHA

03B2 β  GREEK SMALL LETTER BETA

03B3 γ  GREEK SMALL LETTER GAMMA

03B4 δ  GREEK SMALL LETTER DELTA

03B5 ε  GREEK SMALL LETTER EPSILON

03B6 ζ  GREEK SMALL LETTER ZETA

03B7 η  GREEK SMALL LETTER ETA

03B8 θ  GREEK SMALL LETTER THETA

03B9 ι  GREEK SMALL LETTER IOTA

03BA κ  GREEK SMALL LETTER KAPPA

03BB λ  GREEK SMALL LETTER LAMDA

03BC μ  GREEK SMALL LETTER MU

03BD ν  GREEK SMALL LETTER NU

03BE ξ  GREEK SMALL LETTER XI

03BF ο  GREEK SMALL LETTER OMICRON

03C0 π  GREEK SMALL LETTER PI

03C1 ρ  GREEK SMALL LETTER RHO

03C2 ς  GREEK SMALL LETTER FINAL SIGMA

03C3 σ  GREEK SMALL LETTER SIGMA

03C4 τ  GREEK SMALL LETTER TAU

03C5 υ  GREEK SMALL LETTER UPSILON

03C6 φ  GREEK SMALL LETTER PHI

03C7 χ  GREEK SMALL LETTER CHI

03C8 ψ  GREEK SMALL LETTER PSI

03C9 ω  GREEK SMALL LETTER OMEGA

03D1 ϑ  GREEK THETA SYMBOL

03D2 ϒ  GREEK UPSILON WITH HOOK SYMBOL

03D5 ϕ  GREEK PHI SYMBOL

03D6 ϖ  GREEK PI SYMBOL

03DC Ϝ   GREEK LETTER DIGAMMA

03F0 ϰ  GREEK KAPPA SYMBOL

03F1 ϱ   GREEK RHO SYMBOL