Question

The system of equations x-y+3z=4,x+z=2 and x+y-z=0 has
The system of equation​

Answer 1

Answer:

the system of equation has a unique solution

Answer 2

Concept:

A system of linear equations (also known as a linear system) is a collection of one or more linear equations with the same variables in mathematics. The theory of linear systems is the foundation and a key component of linear algebra.

Given:

The system of equations,

x-y+3z = 4, x+z=2 and x+y+z=0.

Find:

Solve this system of linear equations.

Solution:

Solving these linear equations using the matrix method with AX = B.

matrix A = $\left[\begin{array}{ccc}1&-1&3\\1&0&1\\1&1&-1\end{array}\right]$

Matrix X = $\left[\begin{array}{c}x\\y\\z\end{array}\right]$

Matrix B = $\left[\begin{array}{c}4\\2\\3\end{array}\right]$

Determinant of matrix A = 1[(-1×0)-(1×1)]-(-1)[(-1×1) - (1×1)]+ 3[(1×1) - (1×0)]

                                        = 1[0-1] +1 [-1-1] +3{1-0]

                                        = -1 -2 + 3

                                        = 0

Hence, Det(A) is zero. The given system has no solution or infinitely solutions.