Stark

4 b] If Show that

10 c] Solve the system of equations by Gauss elimination method2x+y+4z = 124x+11y-z= 338x-3y+2z = 20

10 b] Test for consistencyx-2y+3z = 23x-y+4z= 42x+y-2z = 5 and hence solve

10 a] Solve the following system of equation by Gauss-Seidel method:20x+y-2z = 173x+20y-z = -182x-3y+20z = 25

9 c] Using power method, find the largest eigenvalue and corresponding eigenvector of the matrix

9 b] By Using Gauss-Jordan method.x+y+z = 92x+y-z = 02x+5y+7z= 52

9 a] Find the rank of the matrix

8 c] (i) Find the remainder when 175 × 113 × 53 is divided by 11. (ii) Solve 𝑥3 + 5𝑥 + 1 = 0(mod 27).

8 b] Solve the system of linear congruence ,x=3(mod 5) , y= 2(mod 6), z= 4(mod 7) Using Remainder Theorem. \

8 a] Using Fermat’s Little Theorem, show that 830 -1 is divisible by 31.