1. Entering matrices: Enter the following three matrices.2 6-5A =B =3 4C =5 32. Check some linear algebra rules:• Is matrix addition commutative? Compute A+B and then B+A. Arethe 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) andaA+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 impliesthat b = e if a + 0. Is that true for matrices? Check by computing A+Band 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 0E = 0 5 00 0 5D =F =0 0 03 34. Create a big matrix with submatrices: The following matrix G is createdby putting matrices A, B, and C, given previously, on its diagonal. In howmany ways can you create this matrix using submatrices A, B, and C (thatis, you are not allowed to enter the nonzero numbers explicitly)?2 6 0 03 9 0 00 0 10 0 3 40 0 0 0 -5 50 0 0 0 5 3G =0 05. Manipulate a matrix: Do the following operations on matrix G created inExercise 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 howMATLAB got that answer?• What happens if you type G(12,1)=1 and hit return?

according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

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)

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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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

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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