Question

Represent the following system of linear equations as a single matrix equation of the form Ax = b, where A is a 3 x 3 matrix and x and b are 3 x 1 column matrices.

x + 3y + 2z = 8
x - y + z = -1
2x+ 3y + 3z = 7

Answer 1

Explanation:

To represent the given system of linear equations as a single matrix equation of the form Ax = b, we need to organize the coefficients of x, y, and z into a matrix A, and the constants on the right side of the equations into a column matrix b.

The system of equations is:

x + 3y + 2z = 8

x - y + z = -1

2x + 3y + 3z = 7

Let's arrange the coefficients of x, y, and z into matrix A:

A = | 1 3 2 |

| 1 -1 1 |

| 2 3 3 |

Now, let's arrange the constants on the right side of the equations into column matrix b:

b = | 8 |

|-1 |

| 7 |

Therefore, the matrix equation of the system is:

A * x = b

where A is the 3x3 matrix:

A = | 1 3 2 |

| 1 -1 1 |

| 2 3 3 |

x is the column matrix:

x = | x |

| y |

| z |

and b is the column matrix:

b = | 8 |

|-1 |

| 7 |

So, the single matrix equation representing the given system of linear equations is:

| 1 3 2 | | x | | 8 |

| 1 -1 1 | * | y | = |-1 |

| 2 3 3 | | z | | 7 |