Explanation: Gauss seidal method is an iterative method. Gauss elimination is based upon the elimination of unknowns. Gauss Jordan is based on back substitution as well as elimination. Factorization is based upon formation of two triangular matrices with a matrix.

Hence x =1, y=3, z=5.

Explanation: Rounding errors generally produces errors while performing numerical computation on the computer. Power fluctuation and operator fatigue are not the general problems which occur in performing numerical computations.

Explanation: Newton Raphson’s method is also known as Tangent Method. It is carried out by drawing a tangent to the curve at the point of initial guess.

This gives the better solution x = 3, y = 1, z = 2, which incidentally is the exact solution.

Explanation: Cramer’s rule is the direct method for solving simultaneous algebraic equations. In other methods, certain iterations are involved and that’s why the process becomes tedious and consequently indirect.

= -54.

Explanation: Inverse acts on product inversely. The inverse operation acting on the product first applies on the last matrix and then moves towards the first matrix if product is of more than two matrices.

Hence, x = 1.64791.

Explanation: The advantage of using Gauss Jordan method is that it involves no labour of back substitution. Back substitution has to be done while solving linear equations formed during solving the problem.

X = -13.

Explanation: This is because singular matrices do not have inverse, because the value of their determinant is zero.

A-1 = \(\frac{1}{6}\begin{pmatrix}2&6&-2\\-3&3&0\\1&-3&2\end{pmatrix}\).

Explanation: Only row transformations are allowed in Gauss Jordan method. Swapping of two rows doesn’t affect the determinant value hence it is allowed here.

Explanation: The Gauss Jordan method reduces an original matrix into a Row Echelon form. In Row Echelon form the matrix is identity.

Hence x=0.33, y=1, z=1.67.

Explanation: Another name for factorization method is Doolittle’s Method as Doolittle’s method is basically an algorithm of Factorization method.

Hence, x = 1.2, y = 2.2, z = 3.2.

Explanation: This is because Cramer’s rule involves division by determinant which should never be equal to 0 leading to not defined numbers.