Inverses: 2x2 Matrices (9.9.2)

Question 1

• An inverse matrix is one that, when multiplied with its original matrix, yields the identity matrix.

Answer 1

• An inverse matrix is one that, when multiplied with its original matrix, yields the identity matrix.

Question 2

• The only matrices that have inverses are those which are square and non-singular:
• A square matrix has the same number of columns as rows.
• A nonsingular matrix is one whose determinant (D) is not 0.

Answer 2

• The only matrices that have inverses are those which are square and nonsingular:
• A square matrix has the same number of columns as rows.
• A nonsingular matrix is one whose determinant (D) is not 0.

Question 3

• To check whether one matrix is the inverse of another, multiply the original matrix with the proposed inverse matrix. If the answer is the identity matrix, then the second matrix is the inverse of the first matrix.

Answer 3

• To check whether one matrix is the inverse of another, multiply the original matrix with the proposed inverse matrix. If the answer is the identity matrix, then the second matrix is the inverse of the first matrix.

Question 4

• To find the inverse of a 2x2 matrix:

A = a b
c d

• Compute its determinant, D.
• Determine the reciprocal of D.
• Multiply the reciprocal with the matrix that has the positions and signs of its elements altered as shown:

A^-1 = 1/D d -b
-c a

Answer 4

• To find the inverse of a 2x2 matrix:

A = a b
c d

• Compute its determinant, D.
• Determine the reciprocal of D.
• Multiply the reciprocal with the matrix that has the positions and signs of its elements altered as shown:

A^-1 = 1/D d -b
-c a