Matrix Operations

Front

What are the dimensions of a matrix with 3 rows and 2 columns?

Back

3 x 2

Front

What must be true in order to ADD two matrices?

Back

The dimensions must be equal.

Front

What is the product of the following matrices? A = [[-1, 2], [3, 4]], B = [[5, 6], [7, 8]]

Back

A * B = [[-1*5 + 2*7, -1*6 + 2*8], [3*5 + 4*7, 3*6 + 4*8]] = [[9, 10], [43, 54]]

Front

Find A + B if A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]]

Back

A + B = [[1+5, 2+6], [3+7, 4+8]] = [[6, 8], [10, 12]]

Front

What is the result of adding the following matrices? A = [[2, 3], [4, 5]], B = [[1, 1], [1, 1]]

Back

A + B = [[2+1, 3+1], [4+1, 5+1]] = [[3, 4], [5, 6]]

Front

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

Back

det(A) = ad - bc

Front

What is the condition for matrix multiplication to be defined?

Back

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

Front

If A is a 2x3 matrix and B is a 3x2 matrix, what are the dimensions of the product AB?

Back

The product AB will be a 2x2 matrix.

Front

What is the identity matrix for 2x2 matrices?

Back

I = [[1, 0], [0, 1]]

Front

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

Back

Multiplying any matrix A by the identity matrix I results in A.