Here is a preview of one type of problem we are going to solve using matrices. Solve this system of equations:

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Presentation transcript:

Here is a preview of one type of problem we are going to solve using matrices. Solve this system of equations:

Here is a preview of one type of problem we are going to solve using matrices. Solve this system of equations: We will rewrite this system of equations in a matrix format:

Here is a preview of one type of problem we are going to solve using matrices. Solve this system of equations: We will rewrite this system of equations in a matrix format: Here A is a coefficient matrix, x is an unknown vector, and b is the vector on the right hand side.

Here is a preview of one type of problem we are going to solve using matrices. Solve this system of equations: We will rewrite this system of equations in a matrix format: Here A is a coefficient matrix, x is an unknown vector, and b is the vector on the right hand side. This is the “augmented matrix” for this system.

Here is a preview of one type of problem we are going to solve using matrices. Solve this system of equations: We will rewrite this system of equations in a matrix format: Here A is a coefficient matrix, x is an unknown vector, and b is the vector on the right hand side. This is the “augmented matrix” for this system. We will want to put it in Reduced Row Echelon Form via a series of simple steps.

Here is a preview of one type of problem we are going to solve using matrices. Solve this system of equations: We will rewrite this system of equations in a matrix format: Here A is a coefficient matrix, x is an unknown vector, and b is the vector on the right hand side. Another way to solve this is to find the “inverse” of matrix A, then multiply through the equation. It will turn out that the inverse will be:

Here is a preview of one type of problem we are going to solve using matrices. Solve this system of equations: We will rewrite this system of equations in a matrix format: Here A is a coefficient matrix, x is an unknown vector, and b is the vector on the right hand side. Another way to solve this is to find the “inverse” of matrix A, then multiply through the equation.