Matrix Operations Mastery

What is the result of multiplying a 2x2 matrix by a 2x1 matrix?

• A scalar value

• A 2x2 matrix

• A 2x1 matrix

• A 3x1 matrix

If A = [[1, 2], [3, 4]] and B = [[5], [6]], what is the product AB?

• [[15], [36]]

• [[17], [39]]

• [[10], [24]]

• [[12], [30]]

Define the determinant of a 2x2 matrix and provide an example.

• The determinant of a 2x2 matrix is always zero.

• The determinant is calculated by adding the products of the diagonal elements.

• For the matrix [[1, 2], [3, 4]], the determinant is 10.

• For the matrix [[2, 3], [1, 4]], the determinant is (2*4) - (3*1) = 8 - 3 = 5.

How do you find the inverse of a 2x2 matrix? Give a brief explanation.

• The inverse is found by swapping the elements and changing the signs.

• The inverse can be calculated by multiplying the matrix by its transpose.

• The inverse is simply the matrix with all elements negated.

• The inverse of a 2x2 matrix is given by (1/det) * [[d, -b], [-c, a]], where det = ad - bc.

When did you find the inverse of the matrix?

• The Matrix should be singular

• The Matrix should be non-singular

• The Matrix should be lower triangular.

• The Matrix should be upper triangular