System of Linear Equation and Matrix Operations

Front

What is a system of linear equations?

Back

A collection of two or more linear equations involving the same variables.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means that there are an infinite number of values that satisfy all equations in the system.

Front

What is matrix multiplication?

Back

A binary operation that produces a new matrix from two matrices by multiplying rows by columns.

Front

What are the conditions for two matrices to be multiplied?

Back

The number of columns in the first matrix must equal the number of rows in the second matrix.

Front

What is a scalar matrix?

Back

A square matrix in which all the elements of the principal diagonal are the same and all other elements are zero.

Front

How do you find the product of two matrices?

Back

Multiply each element of the rows of the first matrix by the corresponding elements of the columns of the second matrix and sum them.

Front

What is the determinant of a 2x2 matrix?

Back

For a matrix [[a, b], [c, d]], the determinant is ad - bc.

Front

What is the inverse of a matrix?

Back

A matrix that, when multiplied with the original matrix, yields the identity matrix.

Front

What is the identity matrix?

Back

A square matrix with ones on the diagonal and zeros elsewhere.

Front

What does it mean for two matrices to be equal?

Back

Two matrices are equal if they have the same dimensions and all corresponding elements are equal.