Question

8 x 9 y = 5 9 x 5 y 4 z = − 3 − 3 x − 3 y 1 0 z = 5 ( a ) Make matrices for A and b such that the system of equations can be expressed as a matrix equation in the form A x = b . ( b ) Is matrix A full rank

Answer 1

A) Matrices for the given system:

A = [[8, 9], [59, 5], [-3, -3], [-3, -3], [5, 10]]

b = [[9], [4z], [1], [z], [5]]

B) Matrix A is not full rank in this case.

Step-by-step explanation:

To express the system of equations in the form of a matrix equation A x = b, we need to arrange the coefficients in a matrix A and the constants on the right side of the equation in a matrix b.

Each row of matrix A corresponds to an equation and each column corresponds to a variable.

Here are the matrices for the given system:

A = [[8, 9], [59, 5], [-3, -3], [-3, -3], [5, 10]]

b = [[9], [4z], [1], [z], [5]]

For matrix A to be full rank, its rows or columns should be linearly independent. Here, the number of columns (2) is less than the number of rows (5), so matrix A is not full rank.