In Exercises 33–36, write each matrix equation as a system...

In Exercises 33–36, write each matrix equation as a system of linear equations without matrices. $$ \left[\begin{array}{ccc}{2} & {0} & {-1} \\ {0} & {3} & {0} \\ {1} & {1} & {0}\end{array}\right]\left[\begin{array}{l}{x} \\ {y} \\ {z}\end{array}\right]=\left[\begin{array}{l}{6} \\ {9} \\ {5}\end{array}\right] $$

In Exercises 33–36, write each matrix equation as a system of linear equations without matrices.
$$
\left[\begin{array}{ccc}{2} & {0} & {-1} \\ {0} & {3} & {0} \\ {1} & {1} & {0}\end{array}\right]\left[\begin{array}{l}{x} \\ {y} \\ {z}\end{array}\right]=\left[\begin{array}{l}{6} \\ {9} \\ {5}\end{array}\right]
$$

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Key Concepts

System of Linear Equations

A system of linear equations is a collection of equations where each equation is linear in the variables. Converting a matrix equation into a system of linear equations involves expressing the result of the matrix multiplication as individual, separate equations for each row, with each equation representing the relationship between the coefficients and the corresponding variable terms.

Matrix Equation

A matrix equation, typically written in the form Ax = b, represents a compact way to express a system of linear equations. Here, A is a matrix containing the coefficients of the variables, x is a column vector of variables, and b is a column vector of constants. This formulation is widely used in linear algebra to simplify and work with multiple linear equations simultaneously.

Matrix Multiplication

Matrix multiplication is the process used to convert the matrix equation into a system of equations. Each entry in the resulting vector is produced by calculating the dot product of a row of the coefficient matrix and the variable vector. This operation allows us to break down the matrix equation into individual scalar equations corresponding to each row.

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