4. Compute the product AB in two ways:(a) by the definition, where Ab₁ and Ab2 are computed separately, and(b) by the row-column rule for computing AB2-4 761-613B=3 50A =

Given: A=2-1-13011 B=-4735 To find: The product AB, by definition, were Ab1 and Ab2 are computed…

Answered: Compute the product AB in two ways: (a)…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 15EQ: 15. Reverse the elementary row operations used in Example 2.9 to show that we can convert

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15. Reverse the elementary row operations used in Example 2.9 to show that we can convert
Write out the addition and multiplication tables for 4.
Show that |a1111a1111a1111a|=(a+3)(a1)3
1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2
- Set up the product Ab1, where b1 is the first column of B. Ab1 = ____ ____ - Calculate Ab1, where b1 is the first column of B. Ab1 = ____ - Set up the product Ab2, where b2 is the second column of B. Ab2 = ____ ____ Calculate Ab2, where b2 is the second column of B. Ab2 = ____
(a) What are the five 2 by 2 reduced matrices R whose entries are all O's and 1's?(b) What are the eight 1 by 3 matrices containing only O's and 1's? Are all eight of them reduced echelon matrices R ?
Create the 10 by 10 second difference matrix K = toepl.itz([2 -1 zeros(l,8 )]). Permute rows and columns randomly by KK = K(randperm(lO), randperm(lO)). Factor by [L, U] = lu(K) and [LL, UU] = lu(K K), and count nonzeros by rmz(L) and nnz(LL ). In this case Lis in perfect tridiagonal order, but not LL.
compute the indicated matrices ( I 2 -D)2
How do I know my adj of A=1? You gave me the formulas for M11 and M22 but what are the formulas for M12, M13, M21, M23, M31, M32, and M33? I wrote all of my sub matrices down that I was given from a previous question that I had asked bartleby and I did not see a pattern.
Q9) Use the construction in the proof of the Chinese remainder theorem to find all solutions to the system of congruences 55x ≡ 2 (mod 3), 55x ≡ 1 (mod 4), and 55x ≡ 3 (mod 5).
You may have been surprised to read (in Thm. 2.12) that for any two integers there is going to be a greatest common divisor which can be written as a linear combination of the two values. In essence, what this says is that since the divisor divides both numbers, there is going to be some combination of multiples of the two that adds up to the divisor. For example, for the numbers 6 and 8, the greatest common divisor is 2 AND 2 = 3(6) + -2(8). Now, I could find that by looking at multiples until a find a combo that would add to 2. That would look like the following. 6 … 12, 18, 24, … 8 … 16, 24 What I would notice is that the 18 and 16 are 2 apart, which means I only need to use some positives and negatives for the coefficients. (This reminds me a lot of the hunt and peck form of factoring we sometimes teach students.) The power of this linear combination is that it gives us a way to write the divisor in terms of the original values we were given. That’s helpful. Which brings us to the…
Prove directly that no number of the form 4a (8b − 1) can be written as the sum of three squares by applying the least integer principle to the set S = {a ∈ N0 | 4a (8b − 1) can be written as the sum of three squares}

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Compute the product AB in two ways: (a) by the definition, where Ab₁ and Ab₂ are computed separately, and (b) by the row-column rule for computing AB A = 2 0 -1 3 11 B = -4 [33 5