Matrix Products: Consider the matrices84- (; " ).3 101B =87and C =1A =741 411010 918Of the possible matrix products ABC, ACB, BAC, BC A, C AB, CBA,which make sense?А. (АСВ, ВАС, СВА) onlyВ. (АВС, ВСА, САВ ) onlyС. (АСВ, ВАС, САВ ) onlyD. all of themE. none of them

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Answered: Matrix Products: Consider the matrices…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.1: Matrix Operations

Problem 20EQ: Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the...

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Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.
If A and B are matrices and AB=0, msut |A|=0 or |B|=0? Explain.
Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the same for each product but varies by warehouse because of the distances involved. It costs $0.75 to distribute one unit from warehouse 1 and $1.00 to distribute one unit from warehouse 2. Organize these costs into a matrix C and then use matrix multiplication to compute the total cost of distributing each product.
Explain what is meant by the minor of an entry in a square matrix.
Find two 22 matrices such that |A|+|B|=|A+B|.
-3 3 1 3 -4 -1] If A = -3 -1 -1 and B = -4 -1, then 3 -4 -3] AB = and ВА - Choose True or False: AB = BA for any two square matrices A and B of the same size.
you notice any čonnectión 3. If A, B and C are matrices with orders, 3 X 3, 2 X 3 and 4 X 2, respectively, which of the following matrix calculations are possible? If the calculation is possible, state the order of the resulting matrix 4B, А + В, 3в" + С, АВ, ВТА, (СВ)", СВА
Matrix Products: Consider the matrices 2 1 (9 5 10 6. 7 A = 7 10 5 7 and C = 3 B 2 10 10 6. 5 5 10 3 3 5 3 5 3 Of the possible matrix products A ВС, АСВ, ВАС, ВСА, САВ, СВА, which make sense? А. (АСВ, ВАС, СВА) only В. (АСВ, ВАС, САВ) only С. (АВС, ВСА, САВ) only D. all of them E. none of them
Matrix Products: Consider the matrices 7 7 8 3 4 1 3 8 В — 9. 4 and C = 7 8 A = 6 4 2 9. 3 1 5 8 4 4 2 9. 6 Of the possible matrix products ABC, ACB, BAC, BC A, C'AB, CBA, which make sense? А. (АСВ, ВАС, СВА) only В. (АВС, ВСА, САВ ) only С. (АСВ, ВАС, САВ ) only D. all of them E. none of them
Find the following matrix product, if possible. 2 60 3]([: [-::]) 1 2 2 4 -4 O A. ·[ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 64 2 -2 64 1([::]-[ 15 B. The product is not possible. 15 4 -4 + 60 - 1 2
43. For square matrices A and B, is it true, in general, that (A + B)-1 = A¯1 + B¯!? Explain. 44. For square matrices A and B, is it true, in general, that (AB)¯1 = A-'B¯!? Explain.
1 =[ -~-;}-·[AB-{] 3 Let A = 1 2 7 16 a. Find A b₁ = 3 1 17 2 20 and b4 O A. The inverse matrix is A-1 = 1 a. Find A and use it solve the four equations Ax=b₁, Ax=b₂,Ax=b3, and Ax=b4. = b. The four equations in part (a) can be solved by the same set of operations, since the coefficient matrix is the same in each case. Solve the four equations in part (a) by row reducing the augmented matrix [A b₁ b2 b3 b4]. 2 2 (Type an integer or simplified fraction for each matrix element.) B. The matrix is not invertible. Select the correct choice below and, if necessary, fill in the answer box to complete your choice

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