In Exercises 35–42, use technology to find the inverse of the given matrix (when it exists). Round all entries in your answer to two decimal places. [Caution: Because of rounding errors, technology sometimes produces an “inverse” of a singular matrix. These often can be recognized by their huge entries.]
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Chapter 4 Solutions
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- Unless otherwise specified, assume that all matrices in these exercises are nxn. Determine which of the matrices in Exercises 1–10 are invertible. Use as few calculations as possible. Justify your answersarrow_forwardIn Exercises 5–8, use the definition of to write the matrix equation as a vector equation, or vice versa.arrow_forwardUse Cramer’s rule to compute the solutions of the systems in Exercises 1–6.arrow_forward
- In Exercises 29–32, find the elementary row operation that trans- forms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first.arrow_forward[M] In Exercises 37–40, determine if the columns of the matrix span R4.arrow_forwardFind the general solutions of the systems whose augmented matrices are given in Exercises 7–14.arrow_forward
- Let matrix B = 5-21 what is The 14-2 3 - 12 2. reduced Yow echelon form of B.arrow_forwardThe bookshop manager at the university has developed a matrix formula for determining the number of Pure and Applied Mathematics textbooks he should order each year. For 2016, the starting point for the formula is the column matrix So. This lists the number of Pure and Applied Mathematies textbooks sold in 2015. 505 Pure 316 Applied Oj is a column matrix listing the number of Mathematics and Physics textbooks to be ordered for 2016. Oj is given by the matrix formula : 01 = A So + B where A= 0.85 0 0.78 80 and B = 75 Determine O1, correct to the nearest integer. a. Given that S, - 499 303 Pure , representing the number of textbooks sold in 2016, b. Applied determine O2 (the numbers of books to be ordered for 2017) using the same matrix equation. The matrix formula above only allows the manager to predict the number of books he should order one year ahead. A new matrix formula enables him to determine the number of books to be ordered two or more years ahead. The new matrix formula is On…arrow_forwardSolve each system in Exercises 1–4 by using elementary rowoperations on the equations or on the augmented matrix. Followthe systematic elimination procedure described in this section.arrow_forward
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