MATHEMATICS FOR ENGINEERING ANALYSIS I 
 MATHEMATICA ASSIGNMENT III
									DUE DATE:    12/13/02

Note: 	1)   You can enter a matrix from Creat Table/Matirx/Palette submenu of the Input menu. In the dialog box, you should choose Matrix and  specify the dimension of your matrix. 
	2) Most commands for matrix operations can be obtained from the Palettes submenu of the File menu. Once you select the Palettes submenu choose the BasicCalculations and from the resulting palette click on the triangular shape infront of Lists and Matrices and then choose Matrix Operations.   
	3) If A and B are matrices, then A + B is their sum, A.B is their product, Det[A] is the determinant of A, Transpose[A] is the transpose of A, Inverse[A] is the inverse of A.  Eigenvalue[A] computes the eigen values of A, while Eigenvector[A]computes the eigen vectors of A.
	4)  A // MatrixForm returns A in the usual matrix form. Thus, at the end of a matrix operation you may want to add // MatrixForm.
	5) LinearSolve[A,b] is the command to solve the system of linear equations given by AX= b. The output has the form {{(Subscript[x, 1])},{(Subscript[x, 2])}, ....}.
	6) To solve a differential equation:  deq = 0, the command is DSolve[  deq == 0, y[x], x ].  When you enter a differential equation, you should write y[x] for y and y'[x] for y', and so on. \(TraditionalForm
      \`DSolve[{\ deq == 0, \ y[x\_0]\  == \ y\_0\ }, \ y[x], x]\) solves the initial value problem  deq = 0, y((Subscript[x, 0])) = (Subscript[y, 0]) .

1.	Let  a = (({{1}, {2}, {-1}}))             b =  (({{2}, {3}}))           A = (({{1, 3}, {2, 4}, {3, 1}}))          B = (({{-1, 2}, {4, -2}, {7, -1}}))   
 	      M = (({{-1, 2, 3}, {0, 4, 5}}))   F =(({{1, 2}, {3, -5}})) 	  G = (({{4, 3, 2}, {1, 0, 1}, {0, 1, 2}}))
	Find each of the following. 	
	a)  3A+4B				b)  AM			
	
	c) MB					d)  b (a^T)	
	
	e)   (G^(-1))				f)  the determinants of F and G	
	
	g) eigen values of Fand G		h)  eigen vectors of F and G	
	
	i)  solve FX = b 			j)  solve  GX = a

2.	Solve each of the following differential equations

	a) y' + y + x =0			b)   x y dx \(\(+\((x\^2 + \ \ 1)\)\)\ dy\  = \ 0
\)

	c) \(TraditionalForm
      \`dy\/dx\  = \ \(x\  - y\  + \ 1\)\/\(x\  + \ y\  - 5\)\), y(0) = 9  		d)   (2  x  + (y^4)) y' = y , y (0) = 1