Matrix Review

Front

What is matrix addition?

Back

Matrix addition involves adding corresponding elements of two matrices of the same dimensions. 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 the product of two matrices A and B?

Back

The product of two matrices A and B (denoted as AB) is calculated by taking the dot product of rows of A with columns of B. The number of columns in A must equal the number of rows in B.

Front

How do you find the element R_3,2 in a matrix R?

Back

To find the element R_3,2, locate the third row and the second column of matrix R. The value at that position is the desired element.

Front

What is a matrix inverse?

Back

A matrix inverse A^-1 is a matrix that, when multiplied by A, yields the identity matrix I. Not all matrices have inverses; a matrix must be square and have a non-zero determinant to have an inverse.

Front

How do you determine if a matrix has an inverse?

Back

To determine if a matrix has an inverse, calculate its determinant. If the determinant is non-zero, the matrix has an inverse; if it is zero, the matrix does not have an inverse.

Front

What is a determinant of a matrix?

Back

The determinant is a scalar value that is a function of the entries of a square matrix. It provides important information about the matrix, such as whether it is invertible.

Front

How do you calculate 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 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 the product of matrices A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]]?

Back

The product AB = [[1*5 + 2*7, 1*6 + 2*8], [3*5 + 4*7, 3*6 + 4*8]] = [[19, 22], [43, 50]].

Front

What does it mean for two matrices to be conformable for multiplication?

Back

Two matrices A (m x n) and B (p x q) are conformable for multiplication if the number of columns in A (n) equals the number of rows in B (p).