Lopez C.P. - Matrix Algebra with Mathematica

The result will be another algebraic expression: In[1]: = Expand [((x + 1) *(x + 2) (x + 2) ^ 2) ^ 3]2 3Out[1] = 8- 12 x- 6 x- x 2) Wecan factor the result of the calculation on the previous example by typing Factor[%] In[2]: = Factor [%]Out[2] = (2 + x) 3) Wecan resolve the indefinite integral of the function (x ^ 2) Sin(x) ^ 2 bytyping Integrate [x ^ 2 Sin [x] ^ 2 x] In[3]:= Integrate[x^2*Sin[x]^2, x]Out[3]=3 2x x Cos[2 x] (1- 2 x) Sin [2 x]--- -------------+ -----------------------6 4 8 4) Wecan find the derivative of the result of the integral above by typing D [% x] In[4]:= D[%, x] Out[4]= 2 2x Cos[2 x] (1 - 2 x ) Cos[2 x]--- -------------+-----------------------2 4 4 5)We can simplify the result of the derivative before typing Simplify [%] In[5]:= Simplify[%]2 2Out[5]= x Sin[x] 6) Wecan develop in power of order 14 series the result from the previous example bytyping Series [% {x, 0.14}] In[6]:= Series[%, {x, 0, 14}]Out[6]=6 8 10 12 144 x 2 x x 2 x 2 x 15x - -- + ---- - -----+-------- - ----------+ O[x]3 45 315 14175 467775 7) We can solve theequation 3ax - 7 x ^ 2 + x ^ 3 = 0 (a, is a parameter) by typing Solve [3ax 7 x^ 2 + x ^ 3 = 0] In[7]:= Solve[3*ax - 7*x^2 + x^3 == 0, x]Out[7]=1/37 49 2{{x->-- + ------------------------------------------------------------------+3 2 1/33 (686 - 81 ax + 9 Sqrt[-1372 ax + 81 ax ] )2 1/3(686 - 81 ax + 9 Sqrt[-1372 ax + 81 ax ] )+ ---------------------------------------------------------------},1/33 21/37 I -49 2{x-> - + - Sqrt[3] (----------------------------------------------------------+3 2 2 1/33(686-81ax+9Sqrt[-1372ax+81ax ] )2 1/3(686 - 81 ax + 9 Sqrt[-1372 ax + 81 ax ] )+ -----------------------------------------------------------------)-1/33 21/349 2- (---------------------------------------------------------------------+2 1/33 (686 - 81 ax + 9 Sqrt[-1372 ax + 81 ax ] )2 1/3(686 - 81 ax + 9 Sqrt[-1372 ax + 81 ax ] )+ ------------------------------------------------------------------)/ 2},1/33 21/37 I -49 2{x-> - - - Sqrt[3] (--------------------------------------------------------+3 2 2 1/33 (686-81ax+9 Sqrt[-1372ax+81ax ] )2 1/3(686 - 81 ax + 9 Sqrt[-1372 ax + 81 ax ] )+ ------------------------------------------------------------------)-1/33 21/349 2- (-----------------------------------------------------------------------+2 1/33 (686 - 81 ax + 9 Sqrt[-1372 ax + 81 ax ] )2 1/3(686 81 ax + Sqrt 9 [1372 ax + 81 ax])+ -----------------------------------------------------------------)/ 2}}1/33 2 8) We can find fivecomplex solutions of the equation x ^ 5 + 2 x + 1 = 0 by typing NSolve [x ^ 5 +2 x + 1 = 0, x] In[8]:= NSolve[x^5 + 2*x + 1 == 0, x]Out[8]= {{x -> -0.7018735688558619 - 0.879697197929824 I},{x -> -0.7018735688558619 + 0.879697197929824 I},{x -> -0.486389035934543},{x -> 0.945068086823133 - 0.854517514439046 I},{{x > 0.945068086823133 + 0.854517514439046 I}} 9) Wecan generate a matrix 3 x 3 whose (i, j) element is 1 / (i+j+1) by typing m =Table [1 / (i + j + 1), {i, 3}, {j, 3}] In[9]:= m = Table[1/(i + j + 1), {i, 3}, {j, 3}]Out[9] = {{1/3, 1/4, 1/5}, {1/4, 1/5, 1/6}, {1/5, 1/6, 1/7}} 10) Wecan invert the matrix above, typing Inverse [m] In[10]: = Inverse [m]Out[10] = {{300, 900, 630}, {900, 2880, 2100}, {630, 2100, 1575}} 11) Wecan find the determinant of the matrix m xIdentidad (3.3) tecleando Det[ m -x IdentityMatrix[3] ] In[11]:= Det[m - x*IdentityMatrix[3]]2 3Out[11] = (1 4755 x + 255600 x - 378000 x ) / 378000 12) Wecan find all the permutations of the three elements {e, f, g} tecleandoPermutations[{e, f, g}]