This is a graded discussion: 10 points possible M3 Explore & Discuss 3 A+ This question comes from Section 2.6, p. 147 in the textbook. Initial Post: Answer the following question to the best of your ability: Suppose A is a square matrix with the property that one of its rows is a nonzero constant multiple of another row. What can you say about the existence or nonexistence of A-1? Explain your answer. Response Posts: Respond to at least two other people in the class. Also makes sure to subscribe to the discussion. If a person responds to your post, make sure to interact with them. Search entries or author Unread ↑ ↓ due - 1 1 it to the form [B]: 101-107 10 0 20 0 0 -1 1 1 -2 0 2 2 --2 2 1 -3 2 1 0 3 -1 -4 2 -1 0 Sthat 2.6 THE INVERSE OF A SQUARE MATRIX 147 Matrices That Have No Inverses If there is a row to the left of the vertical line in the augmented matrix containing all zeros, then the matrix does not have an inverse. 0 A Formula for the Inverse of a 2 × 2 Matrix Before turning to some applications, we show an alternative method that employs a formula for finding the inverse of a 2 X 2 matrix. This method will prove useful in many situations; we will see an application in Example 5. The derivation of this for- mula is left as an exercise (Exercise 62). process when a matrix A does 3 4 2 4 -3 0 0 Formula for the liverse of a 2 x 2 Matrix 1.el 4 A- Suppose Dad be is not exqual to zero. Then A exists and is given by -h DC (14) Note As an aid to memorizing the formula, note that D is the product of the elements along the main thegond minas the product of the elements along the other diagonal: Dad be Man diagonal Next, the matrix Explore and Discuss Suppose A is a square matrix. with the property that one of its rows is a nonzero constant mal- tiple of another row. What can you say about the existence or nonexistence of A? Explain your answer 1 is obtained by interchanging a and d and reversing the signs of b and c. Finally, A¹ is obtained by dividing this matrix by D. EXAMPLE 3 Find the inverse of 4- = Solution We first compute D (1)(4)(2)(3) = 4-6 -2. Next, we rewrite the given matrix, obtaining at comprises the left-hand zero, the latter cannot be clusion that A is singular- termining when the inverse Fertible. 4 -2 3 1 Finally, dividing this matrix by D, we obtain 4 dothers Why are so