Matrix Operations (Add, Subtract, Scalar Multiplication)

Front

What is matrix addition?

Back

Matrix addition is the operation of adding two matrices by adding their corresponding elements. For example, if A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], then A + B = [[1+5, 2+6], [3+7, 4+8]] = [[6, 8], [10, 12]].

Front

What is matrix subtraction?

Back

Matrix subtraction is the operation of subtracting one matrix from another by subtracting their corresponding elements. For example, if A = [[5, 6], [7, 8]] and B = [[1, 2], [3, 4]], then A - B = [[5-1, 6-2], [7-3, 8-4]] = [[4, 4], [4, 4]].

Front

What is scalar multiplication of a matrix?

Back

Scalar multiplication involves multiplying each element of a matrix by a scalar (a single number). For example, if k = 3 and A = [[1, 2], [3, 4]], then kA = [[3*1, 3*2], [3*3, 3*4]] = [[3, 6], [9, 12]].

Front

Can you add matrices of different dimensions?

Back

No, you cannot add matrices of different dimensions. The matrices must have the same number of rows and columns.

Front

What is an augmented matrix?

Back

An augmented matrix is a matrix that represents a system of linear equations, including the coefficients and the constants from the equations. For example, the system x + y = 2 and 2x + 3y = 5 can be represented as the augmented matrix [[1, 1, 2], [2, 3, 5]].

Front

How do you find the result of A + B if A = [[2, 3], [4, 5]] and B = [[1, 1], [1, 1]]?

Back

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

Front

What is the result of B - A if A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]]?

Back

B - A = [[5-1, 6-2], [7-3, 8-4]] = [[4, 4], [4, 4]].

Front

What is the result of scalar multiplication if k = 2 and A = [[3, 4], [5, 6]]?

Back

kA = [[2*3, 2*4], [2*5, 2*6]] = [[6, 8], [10, 12]].

Front

What happens if you try to add a 2x3 matrix to a 3x2 matrix?

Back

You cannot add a 2x3 matrix to a 3x2 matrix because their dimensions do not match.

Front

What is the formula for scalar multiplication of a matrix?

Back

If A is a matrix and k is a scalar, then kA = [[k*a_{11}, k*a_{12}, ...], [k*a_{21}, k*a_{22}, ...], ...] where a_{ij} are the elements of matrix A.