Question

write the given system of linear equations as a matrix equation of the form ax = b. x1 − 3x2 4x3 = 0 3x1 x2 − 6x3 = 5 x1 x2 x3 = 0

Answer 1

To convert the provided system of linear equations into a matrix equation AX = B, coefficients are placed into matrix A, the variables into vector X, and the constants into vector B. The resulting matrix and vectors represent the equation in the desired format.

Step-by-step explanation:

To write the given system of linear equations as a matrix equation of the form AX = B, we need to represent the coefficients of the variables in matrix form, the variables themselves in a vector, and the constants in another vector. Given the system:

• x1 - 3x2 + 4x3 = 0
• 3x1 - x2 - 6x3 = 5
• x1 + x2 + x3 = 0

The matrix A will contain the coefficients of the variables:

A =
| 1 -3 4 |
| 3 -1 -6 |
| 1 1 1 |

The vector X will contain the following variables:

X =
| x1 |
| x2 |
| x3 |

The vector B will contain the constants from the right side of the equations:

B =
| 0 |
| 5 |
| 0 |

Putting it all together, the matrix equation is AX = B.