# Linear Algebra - Linear Algebra

51:

The solution of the given matrix equation is

 A. x1=0, x2=0, x3=0 B. x1=1, x2=1, x3=0 C. x1=0, x2=1, x3=1 D. x1=2, x2=-5, x3=-1 Answer Report Discuss Option: A Explanation : Let matrices AX = B Multiplying both sides by A-1 X = A-1B But as B = 0 therfore X = 0 Hence x1 = 0, x2 = 0, x3 = 0 Click on Discuss to view users comments. Write your comments here:
52:

If product of matrix

is a null matrix, then θ and Φ differ by an

 A. odd multiple of π B. even multiple of π C. odd multiple of π/2 D. even multiple of π/2 Answer Report Discuss Option: C Explanation : A null matrix, when cos  i.e. if    is an odd miltiple of  Click on Discuss to view users comments. Write your comments here:
53:

Sum of the eigen values of the matrix

for real and negative values of x is

 A. greater than zero B. less than zero C. zero D. dependent on value of x Answer Report Discuss Option: A Explanation : Eigen values are given by the solution of equation Since x is real and negative, put x = -k, where k is positive constant If λ1 and λ2 be the solutions of the above equations then λ1 and λ2 are eigen values. Now sum of eigen values = sum of roots of the above equation = 4 (> 0 )   Click on Discuss to view users comments. Write your comments here:
54:

The system of equations

4x + 6y = 8

7x + 8y = 9

3x + 2y = 1

has

 A. no solutions B. only one solution C. two solutions D. infinite number of solutions Answer Report Discuss Option: B Explanation : For given system of equations = 4 (8 - 18) - 6 (7 - 27) + 8 (14 - 24) = -40 + 120 - 80 = 0 Since  = 0, hence given system of equations has unique solution, i.e. only one solution. Click on Discuss to view users comments. Write your comments here:
55:

The system of equations

4x + 6y = 8

7x + 8y = 9

3x + 2y = 1

has

 A. no solutions B. only one solution C. two solutions D. infinite number of solutions Answer Report Discuss Option: B Explanation : For given system of equations = 4 (8 - 18) - 6 (7 - 27) + 8 (14 - 24) = -40 + 120 - 80 = 0 Since  = 0, hence given system of equations has unique solution, i.e. only one solution. Click on Discuss to view users comments. Write your comments here: