Unit 13 Matrices - Multiplication & Inverses

Front

What is the condition for multiplying two matrices A (m x n) and B (p x q)?

Back

Matrix multiplication is defined if the number of columns in A (n) is equal to the number of rows in B (p).

Front

Can a 2x3 matrix be multiplied by a 3x12 matrix?

Back

Yes, a 2x3 matrix can be multiplied by a 3x12 matrix because the number of columns in the first matrix (3) matches the number of rows in the second matrix (3).

Front

What is the result of multiplying a 2x3 matrix by a 3x2 matrix?

Back

The result is a 2x2 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

What is the identity matrix?

Back

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

Front

Are the matrices [[1, 2], [3, 4]] and [[4, -2], [-3, 1]] inverses of each other?

Back

No, they are not inverses of each other.

Front

What does it mean if two matrices are not compatible for multiplication?

Back

It means that the number of columns in the first matrix does not equal the number of rows in the second matrix.

Front

If matrix A is 2x3 and matrix B is 3x4, what is the dimension of the product AB?

Back

The dimension of the product AB will be 2x4.

Front

What is the result of multiplying a matrix by a zero matrix?

Back

The result is a zero matrix of appropriate dimensions.

Front

What is the determinant of a 2x2 matrix [[a, b], [c, d]]?

Back

The determinant is ad - bc.