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Chapter 1: Problem 3

Determine the size and contents of the following arrays. Note that the later arrays may depend on the definitions of arrays defined earlier in this exercise. a. \(a=1: 2: 5\); b. \(b=\left\\{a^{+} a^{*} a^{*}\right\\}\) c. \(c=b(1: 2: 3,1: 2: 3)\); d. \(d=a+b(2,:)=\) c. \(w=\) [zeros \((1,3)\) ones \((3,1), 3: 5^{*}\) ? f. \(b([1] 3], 2)=b([3,1], 2)=\)

Short Answer

Expert verified
In summary: - Array \(a = [1, 3, 5]\) - Array \(b = [+1, +3, +5, -1, -3, -5, -1, -3, -5]\) - Array \(c = \begin{bmatrix}1 & 3 & 5\\ -1 & -3 & -5\\ -1 & -3 & -5\end{bmatrix}\) - Array \(d = [0, 0, 0]\) - Array \(w = \begin{bmatrix}0 & 0 & 0 & 1 & 3 & 3+\sqrt{5} & 5\end{bmatrix}\) - Arrays b([1] 3], 2) and b([3, 1], 2) are equal to \([3, -3]\) and \([-3, 3]\), respectively.

Step by step solution

01

2a. Analyze Array a

Array a is defined as a range of elements from \(1\) to \(5\) with increments of \(2\): \(a = 1:2:5\)
02

2b. Calculate and Construct Array a

To construct array a, let's start with the first element which is \(1\) and increment it by \(2\). 1. \(a(1) = 1\) 2. \(a(2) = a(1) + 2 = 3\) 3. \(a(3) = a(2) + 2 = 5\) So, array a is: \[a = [1, 3, 5]\]
03

2c. Analyze Array b

Array b is defined as \(\{a^{+} a^{*} a^{*}\}\), which is a different combination of operations on array a.
04

2d. Calculate and Construct Array b

To find array b, we concatenate positive and negative elements of array a twice. \(b = [+1, +3, +5, -1, -3, -5, -1, -3, -5]\)
05

2e. Analyze Array c

Array c is a sub-array of b obtained by taking elements in the positions from the first to the third, with increments of 2, and stacking them as rows: \[c = b(1:2:3, 1:2:3)\]
06

2f. Calculate and Construct Array c

To create array c, let's take elements of array b at the positions we calculated above and stack them as rows: \(c = \begin{bmatrix}b(1) & b(2) & b(3)\\ b(1+2) & b(2+2) & b(3+2)\\ b(1+4) & b(2+4) & b(3+4)\end{bmatrix} = \begin{bmatrix}1 & 3 & 5\\ -1 & -3 & -5\\ -1 & -3 & -5\end{bmatrix}\)
07

2g. Analyze Array d

Array d is a sum of two arrays: the elements in the second row of array b, and array a itself: \(d = a + b(2, :)\)
08

2h. Calculate and Construct Array d

To find array d, let's add the second row of array b to array a: \(d = [1, 3, 5] + [-1, -3, -5] = [0, 0, 0]\)
09

2i. Analyze Array w

Array w is created by concatenating three different arrays: 1. A 1 by 3 matrix filled with zeros, denoted as zeros(1,3) 2. A 3 by 1 matrix filled with ones, denoted as ones(3,1) 3. The range from \(3\) to \(5^{*}\)
10

2j. Calculate and Construct Array w

Array w is a concatenation of three different arrays: 1. zeros(1,3) = \(\begin{bmatrix}0 & 0 & 0\end{bmatrix}\) 2. ones(3,1) = \(\begin{bmatrix}1 \\ 1 \\ 1\end{bmatrix}\) 3. The range from \(3\) to \(5^{*}\), which means we start with 3 and increment by \(\sqrt{5}\). \(w = \left[ \begin{bmatrix}0 & 0 & 0 \end{bmatrix}, \begin{bmatrix}1 \\ 1 \\ 1\end{bmatrix}, \begin{array}{c}3 \\ 3 + \sqrt{5} \\ 5\end{array} \right] = \begin{bmatrix}0 & 0 & 0 & 1 & 3 & 3 + \sqrt{5} & 5\end{bmatrix}\)
11

2k. Analyze Arrays b([1] 3], 2) and b([3, 1], 2)

We need to find elements of array b, with the positions specified, and create two new arrays based on these elements.
12

2l. Calculate and Construct Arrays b([1] 3], 2) and b([3, 1], 2)

Using elements of array b, let's calculate and construct the required arrays: 1. b([1] 3], 2) = \([b(1, 2), b(3, 2)] = [3, -3]\) 2. b([3, 1], 2) = \([b(3, 2), b(1, 2)] = [-3, 3]\)

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Most popular questions from this chapter

Solve the following system of simultaneous equations for \(x\). \(-2.0 x_{1}+5.0 x_{2}+1.0 x_{3}+3.0 x_{4}+4.0 x_{5}-1.0 x_{6}=0.0\) \(2.0 x_{1}-1.0 x_{2}-5.0 x_{3}-2.0 x_{4}+6.0 x_{5}+4.0 x_{6}=1.0\) \(-1.0 x_{1}+6.0 x_{2}-4.0 x_{3}-5.0 x_{4}+3.0 x_{5}-1.0 x_{6}=-6.0\) \(4.0 x_{1}+3.0 x_{2}-6.0 x_{3}-5.0 x_{4}-2.0 x_{5}-2.0 x_{6}=10.0\) \(-3.0 x_{1}+6.0 x_{2}+4.0 x_{3}+2.0 x_{4}-6.0 x_{5}+4.0 x_{6}=-6.0\) \(2.0 x_{1}+4.0 x_{2}+4.0 x_{3}+4.0 x_{4}+5.0 x_{5}-4.0 x_{6}=-2.0\)

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