ASMT 6.2 Add and Subtract Matrices

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are defined by the number of rows and columns it contains, expressed as 'rows x columns'. For example, a matrix with 3 rows and 2 columns is said to have dimensions 3x2.

Front

Can you add or subtract matrices of different dimensions?

Back

No, you cannot add or subtract matrices unless they have the same dimensions.

Front

How do you subtract two matrices?

Back

To subtract two matrices, subtract the corresponding elements from each other. For example, if A = [[1, 2], [3, 4]] and B = [[4, 3], [2, 1]], then A - B = [[1-4, 2-3], [3-2, 4-1]] = [[-3, -1], [1, 3]].

Front

What is the result of subtracting the matrices [[3, -8], [0, -1]] and [[3, -4], [8, -13]]?

Back

The result is [[3-3, -8-(-4)], [0-8, -1-(-13)]] = [[0, -4], [-8, 12]].

Front

What is the result of subtracting the matrices [[3, -8], [0, -1]] and [[3, -4], [8, -13]]?

Back

The result is [[3-3, -8-(-4)], [0-8, -1-(-13)]] = [[0, -4], [-8, 12]].

Front

What is a zero matrix?

Back

A zero matrix is a matrix in which all the elements are zero. It serves as the additive identity in matrix addition.

Front

What is the additive identity in matrix addition?

Back

The additive identity is the zero matrix, which, when added to any matrix, does not change the value of that matrix.

Front

Can you multiply matrices of different dimensions?

Back

Yes, but only if the number of columns in the first matrix is equal to the number of rows in the second matrix.

Front

What is the result of adding the matrices [[1, 2], [3, 4]] and [[5, 6], [7, 8]]?

Back

The result is [[1+5, 2+6], [3+7, 4+8]] = [[6, 8], [10, 12]].

Front

What is a 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 is a scalar and A = [[1, 2], [3, 4]], then kA = [[k*1, k*2], [k*3, k*4]].