Unit 9 Test Matrices

Front

What is the definition of a matrix inverse?

Back

The inverse of a matrix A is another matrix, denoted A^{-1}, such that when A is multiplied by A^{-1}, the result is the identity matrix I, i.e., A * A^{-1} = I.

Front

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

Back

Front

What is the result of adding two matrices?

Back

The result of adding two matrices A and B of the same dimensions is a new matrix C, where each element C_{ij} = A_{ij} + B_{ij}.

Front

What is the identity matrix?

Back

Front

What is the determinant of a 2x2 matrix?

Back

Front

What is the result of multiplying a matrix by its inverse?

Back

Front

What is scalar multiplication of a matrix?

Back

Scalar multiplication involves multiplying each element of a matrix by a scalar (a constant). For example, if k is a scalar and A is a matrix, then kA is obtained by multiplying each element of A by k.

Front

What is the formula for the inverse of a 2x2 matrix with specific values?

Back

Front

What is matrix addition?

Back

Matrix addition is the operation of adding two matrices by adding their corresponding elements. The matrices must have the same dimensions.

Front

What is the significance of the determinant in finding the inverse of a matrix?

Back

The determinant must be non-zero for a matrix to have an inverse. If the determinant is zero, the matrix is singular and does not have an inverse.