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 3x2 matrix has 3 rows and 2 columns.

Front

How do you subtract two matrices?

Back

To subtract two matrices, subtract corresponding elements. For example, if A = [[3, -8], [0, -1]] and B = [[1, 3], [4, 5]], then A - B = [[3-1, -8-3], [0-4, -1-5]] = [[2, -11], [-4, -6]].

Front

How do you multiply two matrices?

Back

To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. The element in the resulting matrix is the dot product of the corresponding row and column.

Front

What is the number of rows in a 7 x 3 matrix?

Back

A 7 x 3 matrix has 7 rows.

Front

What is the result of subtracting the matrices [[-5], [-8], [3], [10]] and [[-9], [8], [3], [2]]?

Back

The result is [[-5 - (-9)], [-8 - 8], [3 - 3], [10 - 2]] = [[4], [-16], [0], [8]].

Front

What is a zero matrix?

Back

A zero matrix is a matrix in which all the elements are zero. It is denoted as O and can be of any size.

Front

What is the identity matrix?

Back

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

Front

What is a transpose of a matrix?

Back

The transpose of a matrix is obtained by swapping its rows and columns. If A is a matrix, then its transpose is denoted as A^T.

Front

What is the determinant of a 2x2 matrix?

Back

For a 2x2 matrix A = [[a, b], [c, d]], the determinant is calculated as det(A) = ad - bc.

Front

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