Question

Consider the following matrix. A = 1 k 3 −5 6 1 Assume that the matrix is the augmented matrix of a system of linear equations. Determine the number of equations and the number of variables.

Answer 1

The augmented matrix is of two equations, and two variables.

Explanation:

This is an augmented matrix, which means the constant terms are on the last column.

The matrix can be written as

X1 + kX2 = 3

-5X1 + 6X2 = 1

The constants are 3, 1, and all the coefficients of the variables, X1 and X2.

X1 and X2 can take any values.

k is constant, just like 1, -5, and 6.

Though, it is not specified, the consistency or inconsistency of the equation depends on the value k takes.