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1. Entering matrices: Enter the following three matrices. A= []. D-[! ). c. 2 6 2 -5 5 3 9 3 4 2. Check some linear algebra rules: • Is matrix addition commutative? Compute A+B and then B+A. Are the results the same? • Is matrix addition associative? Compute (A+B)+C and then A+(B+C) in the order prescribed. Are the results the same? • Is multiplication with a scalar distributive? Compute a (A+B) and QA+aB, taking a = 5, and show that the results are the same. • Is multiplication with a matrix distributive? Compute A* (B+C) and compare with A+B+A+C.

1. Entering matrices: Enter the following three matrices. A= []. D-[! ). c. 2 6 2 -5 5 3 9 3 4 2. Check some linear algebra rules: • Is matrix addition commutative? Compute A+B and then B+A. Are the results the same? • Is matrix addition associative? Compute (A+B)+C and then A+(B+C) in the order prescribed. Are the results the same? • Is multiplication with a scalar distributive? Compute a (A+B) and QA+aB, taking a = 5, and show that the results are the same. • Is multiplication with a matrix distributive? Compute A* (B+C) and compare with A+B+A+C.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1. Entering matrices: Enter the following three matrices. 2 6 -5 A = B = 3 4 C = 5 3 2. Check some linear algebra rules: • Is matrix addition commutative? Compute A+B and then B+A. Are the results the same? • Is matrix addition associative? Compute (A+B) +C and then A+(B+C) in the order prescribed. Are the results the same? • Is multiplication with a scalar distributive? Compute a (A+B) and aA+aB, taking a = 5, and show that the results are the same. • Is multiplication with a matrix distributive? Compute A (B+C) and compare with A*B+A+C. • Matrices are different from scalars! For scalars, ab = ac implies that b = e if a + 0. Is that true for matrices? Check by computing A+B and A*C for the matrices given in Exercise 1. Also, show that A*B + B*A. 3. Create matrices with zeros, eye, and ones: Create the following matri- ces with the help of the matrix generation functions zeros, eye, and ones. See the on-line help on these functions, if required (e.g., help eye). 5 0 E = 0 5 0 0 0 5 D = F = 0 0 0 3 3 4. Create a big matrix with submatrices: The following matrix G is created by putting matrices A, B, and C, given previously, on its diagonal. In how many ways can you create this matrix using submatrices A, B, and C (that is, you are not allowed to enter the nonzero numbers explicitly)? 2 6 0 0 3 9 0 0 0 0 1 0 0 3 4 0 0 0 0 -5 5 0 0 0 0 5 3 G = 0 0 5. Manipulate a matrix: Do the following operations on matrix G created in Exercise 4. • Delete the last row and last column of the matrix. • Extract the first 4 x 4 submatrix from G. • Replace G(5,5) with 4. • What do you get if you type G(13) and hit return? Can you explain how MATLAB got that answer? • What happens if you type G(12,1)=1 and hit return?
Transcribed Image Text:1. Entering matrices: Enter the following three matrices. 2 6 -5 A = B = 3 4 C = 5 3 2. Check some linear algebra rules: • Is matrix addition commutative? Compute A+B and then B+A. Are the results the same? • Is matrix addition associative? Compute (A+B) +C and then A+(B+C) in the order prescribed. Are the results the same? • Is multiplication with a scalar distributive? Compute a (A+B) and aA+aB, taking a = 5, and show that the results are the same. • Is multiplication with a matrix distributive? Compute A (B+C) and compare with A*B+A+C. • Matrices are different from scalars! For scalars, ab = ac implies that b = e if a + 0. Is that true for matrices? Check by computing A+B and A*C for the matrices given in Exercise 1. Also, show that A*B + B*A. 3. Create matrices with zeros, eye, and ones: Create the following matri- ces with the help of the matrix generation functions zeros, eye, and ones. See the on-line help on these functions, if required (e.g., help eye). 5 0 E = 0 5 0 0 0 5 D = F = 0 0 0 3 3 4. Create a big matrix with submatrices: The following matrix G is created by putting matrices A, B, and C, given previously, on its diagonal. In how many ways can you create this matrix using submatrices A, B, and C (that is, you are not allowed to enter the nonzero numbers explicitly)? 2 6 0 0 3 9 0 0 0 0 1 0 0 3 4 0 0 0 0 -5 5 0 0 0 0 5 3 G = 0 0 5. Manipulate a matrix: Do the following operations on matrix G created in Exercise 4. • Delete the last row and last column of the matrix. • Extract the first 4 x 4 submatrix from G. • Replace G(5,5) with 4. • What do you get if you type G(13) and hit return? Can you explain how MATLAB got that answer? • What happens if you type G(12,1)=1 and hit return?
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