Matrix Operations & Solving Systems

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers arranged in rows and columns.

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in the form 'rows x columns', indicating how many rows and how many columns it has.

Front

How do you add two matrices?

Back

To add two matrices, they must have the same dimensions. Add corresponding elements together.

Front

What is a zero matrix?

Back

A zero matrix is a matrix in which all elements are zero.

Front

What is the identity matrix?

Back

An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.

Front

How do you multiply a matrix by a scalar?

Back

To multiply a matrix by a scalar, multiply each element of the matrix by the scalar.

Front

What is the result of multiplying a 2x2 matrix by a 2x3 matrix?

Back

The result will be a 2x3 matrix.

Front

What is the inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted A^-1, such that A * A^-1 = I, where I is the identity matrix.

Front

How do you find the inverse of a 2x2 matrix?

Back

For a 2x2 matrix [[a, b], [c, d]], the inverse is (1/(ad-bc)) * [[d, -b], [-c, a]], provided ad-bc ≠ 0.

Front

What is a determinant?

Back

The determinant is a scalar value that can be computed from the elements of a square matrix and provides information about the matrix, such as whether it is invertible.