Solving a System of Equations with Inverses (9.9.5)

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 that are square and nonsingular.
• A square matrix has the same number of columns as it has rows.
• A nonsingular matrix is one whose determinant D is not 0.

Answer 2

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

Question 3

• The inverse of a 2x2 matrix : A= a b A^-1= 1/d d -b
-c d -c a,

where D is the determinant of A.

Answer 3

• The inverse of a 2x2 matrix : A= a b A^-1= 1/d d -b
-c d -c a,

where D is the determinant of A.