Solving System of Linear Equations Using Inverse

Q.

How do you solve a matrix with variables?

Q. The system of equations x + ky + 3z = 0, 3x + ky - 2z = 0, 2x + 3y - 4z = 0 possess a non-trivial solution over the set of rationals, then 2k is an integral element of the interval

1. [10, 20]
2. (20, 30)
3. [30, 40]
4. (40, 50)

Q.

The equation x + 2y + 5z = 0 has a trivial solution

1. True

2. False

Q.

For a system of n linear equations in n variables, let A, B and X represent the coefficient, constant and variable matrices.If $\left|A\right|=0$, and (adj A). B $\ne$ 0 the system of equations is inconsistent and has no solution.

1. True

2. False

Q.

The given set of equations has at least one non trivial solution.

x + 3y + 2z =0

2x + y + 4z = 0

x + 11y + 14z =0

1. True

2. False

Q.

For a system of n non homogeneous equations in n variables equations let A, B and X represent the coefficient, constant and variable matrices. Then,

If $\left|A\right|\ne$ 0, then X = $A^{-1}$ B gives a trivial solution.

1. True

2. False

Q.

An undetermined set of linear equations is always inconsistent.

1. True

2. False

Q.

Match the possible scenarios for system of linear equations in 3 variables.

$\begin{array}{cc}ColumnI& ColumnII\\ a.Underdeterminedsystem& i.Nosolution\\ b.Overdeterminedsystem& ii.Singlesolution\\ c.Exactlydeterminedsystem& iii.Infinitesolution\end{array}$

1. a – i, ii; b-i, ii; c-ii, iii

2. a – i, ii; b-i, ii; c-ii, iii

3. a – i, iii; b-i, ii, iii; c-i, ii, iii

4. a – iii, b-i, ii; c-i, ii, iii