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Matrices: FAQ

Frequently asked questions about matrices

What is a matrix?

A matrix is a rectangular array of numbers arranged in rows and columns.
Matrices can be useful for organizing and manipulating data. They can also be used as a tool to help solve systems of equations.

How do we multiply a matrix by a scalar?

To multiply a matrix by a scalar, we multiply each entry in the matrix by the scalar. For example, if
A=[2314]
and we want to multiply A by 2, we can multiply each entry by 2 to get:
2A=[4628]

How do we add or subtract two matrices?

To add or subtract two matrices, we add or subtract corresponding entries. So if
A=[2314]
and
B=[5231],
then
A+B=[7545]
and
AB=[3123]

How do we multiply two matrices together?

This one's a bit trickier. To multiply two matrices together, we take the dot product of the rows from the first matrix with the columns from the second matrix. The result is a new matrix. For example, if
A=[2314]
and
B=[5231],
then
AB=[25+3322+3115+4312+41]=[197176].

What can we do with the inverse of a matrix?

Finding the inverse of a matrix can be useful for solving linear systems of equations. If A is the matrix representing the system of equations, and b is the vector of solutions, then Ax=b. If we can find the inverse of A, we can multiply both sides of the equation by it to isolate x:
A1Ax=A1bx=A1b.

Where are matrices used in the real world?

Matrices have tons of real-world applications! They can be used in computer graphics to perform transformations on images, in physics to model physical systems, and in statistics to analyze data, just to name a few.

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