Front

What is a matrix?

Back

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

Front

How do you represent a system of equations using matrices?

Back

A system of equations can be represented using an augmented matrix, where the coefficients of the variables form the left part and the constants form the right part.

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in the form 'rows x columns', indicating the number of rows and the number of columns.

Front

What is the result of adding two matrices?

Back

The result of adding two matrices is a new matrix where each element is the sum of the corresponding elements from the two matrices, provided they have the same dimensions.

Front

What is matrix multiplication?

Back

Matrix multiplication involves taking the dot product of rows and columns from two matrices, resulting in a new matrix.

Front

Can you multiply a 2x3 matrix by a 3x2 matrix?

Back

Yes, you can multiply a 2x3 matrix by a 3x2 matrix, resulting in a 2x2 matrix.

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere, serving as the multiplicative identity in matrix multiplication.

Front

What is the determinant of a matrix?

Back

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

Front

What does it mean for matrices to be equal?

Back

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

Front

What is a transpose of a matrix?

Back

The transpose of a matrix is formed by flipping it over its diagonal, turning rows into columns and vice versa.