Verifying the Inverse of a Matrix Calculate the products AB and BA to verify that B is the inverse of A.
Trending nowThis is a popular solution!
Chapter 6 Solutions
College Algebra
- Finding a Value: Find x such that the matrix is equal to its own inverse. A=3x23arrow_forwardGuided Proof Prove that the inverse of a symmetric non-singular matrix is symmetric. Getting Started: To prove that the inverse of A is symmetric, you need to show that A-1T=A-1. i Let A be symmetric, nonsingular matrix. ii This means that AT=A and A-1 exists. iii Use the properties of the transpose to show that A-1T is equal to A-1.arrow_forwardConjecture Consider matrices of the form Aa11000...00a2200...000a330...00000...ann. (a) Write a 22 matrix and a 33 matrix in the form of A. Find the inverse of each. (b) Use the result of part (a) to make a conjecture about the inverses of matrices in the form of A.arrow_forward
- Guided proof Prove the associative property of matrix addition: A+B+C=A+B+C. Getting Started: To prove that A+B+C and A+B+C are equal, show that their corresponding entries are equal. i Begin your proof by letting A, B, and C be mn matrices. ii Observe that the ij th entry of B+C is bij+cij. iii Furthermore, the ij th entry of A+B+C is aij+bij+cij. iv Determine the ij th entry of A+B+C.arrow_forwardGuided Proof Prove that if A is row-equivalent to B, and B is row-equivalent to C, A is row-equivalent to C. Getting Started: to prove that If A is row-equivalent to C, you have to find elementary matrices E1, E2. Ek such that A=EkE2E1C. i Begin by observing that A is row-equivalent to B and B is row-equivalent to C. ii This means that there exist elementary matrices F1F2Fn and G1G2Gm such that A=FnF2F1B and B=GmG2G1C. iii Combine the matrix equations from step ii.arrow_forwardGuide Proof Prove that if A and B are diagonal matrices of the same size, then AB=BA. Getting Started: To prove that the matrices AB and BA are equal, you need to show that their corresponding entries are equal. i Begin your proof by letting A=aij and B=bij be two diagonal nn matrices. ii The ij th entry of the product AB is cij=k=1naikbkj. iii Evaluate the entries cij for the two cases ij and i=j. iv Repeat this analysis for the product BA.arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning