Linear Algebra Answers

define T: R3→R3 by
. T(x, y, x)=(x+y, y, 2x-2y+2z)
Check that T satisfies the polynomial (x-1)square(x-2). Find the minimal polynomial of T.

1/4 x+3/8 y=-1
x+y=0

Determine all values of the constant a for which the following system has (a) no
solution, (b) an infinite number of solutions, and (c) a unique solution.
ax1 + x2 + x3 = 1,
x1 + ax2 + x3 = 1,
x1 + x2 + ax3 = 1.

solve the system of equations
8x1 -x2 +2x3 =4
-3x1 +11x2 -x3 +3x4 =23
_x2 +10x3 -x4 =-13
_2x1 +x2 -x3 +8x4 =13
with x^(0) =[0 0 0 0]^T by using the Gauss Jacoboi and Gauss Seidel method. The exact solution of the system is x=[1 2 -1 1]^T. Perform the required number of iteration so that the same accuracy is obtained by birth the methods. What conclusions can you draw from the result obtained?

Which of the following statement are True.(1) if a matrix has n^2 entries , where n belongs to N , then it is a square matrix.

Is Cramer 's Rule applicable for solving the linear system below? If yes, apply it. Otherwise, alter the last equation in the system so that the solution can be obtained by applying the rule.
x+y+z=π
-πx +πy+ √2 z =0
π^2 x+ π^2 y+2z =0.

Give example, with justification , of the following: (1) two non -zero ,3×3 matrices A and B , with|A| =0, |B|= (5/7)i ; (2) . two non - singular 2×2 matrices C and D , with |C| = √2 |D| ?

If a and b are non-collinear vectors and A = (x+y)a + (2x + y+1)b. Find x and y

Find the inverse of the matrix A =[1 - 1 1, 1 - 2 4, 1 2 2] by gauss Jordan method.