Question

Answer the following questions for the array shown below. $$ \text { array } 1=\left[\begin{array}{rrrrr} 1.1 & 0.0 & 2.1 & -3.5 & 6.0 \\ 0.0 & 1.1 & -6.6 & 2.8 & 3.4 \\ 2.1 & 0.1 & 0.3 & -0.4 & 1.3 \\ -1.4 & 5.1 & 0.0 & 1.1 & 0.0 \end{array}\right] $$ a. What is the size of array2? b. What is the value of array \(1(4,2)\) ? c. What is the size and value of array \(1(:, 2: 2)\) ? d. What is the size and value of array \(1([13]\), end) ?

Short answer

a. Size of array1: 4 x 5 b. Value of array \(1(4,2)\): 5.1 c. Size of array \(1(:, 2: 2)\): 4 x 1; Value of array \(1(:, 2: 2)\): \[ \left[\begin{array}{r} 0.0 \\ 1.1 \\ 0.1 \\ 5.1 \end{array}\right] \] d. Size of array \(1([1 3], \text{end})\): 2 x 1; Value of array \(1([1 3], \text{end})\): \[ \left[\begin{array}{r} 6.0 \\ 1.3 \end{array}\right] \]

Step-by-step solution

Part (a): Finding the size of the array1

To find the size of an array, we need to count the number of rows and the number of columns. In this case, we can see that array1 has 4 rows and 5 columns. So the size of array1 is: Size of array1: 4 x 5

Part (b): Finding the value of array \(1(4,2)\)

To find the value of array \(1(4,2)\), we need to look at the element in the 4th row and the 2nd column of array1. The element at this position is 5.1. So: Value of array \(1(4,2)\): 5.1

Part (c): Finding the size and value of array \(1(:, 2: 2)\)

To find the size and value of array \(1(:, 2: 2)\), we need to understand colon notation. Colon means all elements along that dimension. In this case, we want all rows but only the 2nd column. The array we are looking for will have the following elements: $$ \left[\begin{array}{r} 0.0 \\ 1.1 \\ 0.1 \\ 5.1 \end{array}\right] $$ Size of array \(1(:, 2: 2)\): 4 x 1 Value of array \(1(:, 2: 2)\): $$ \left[\begin{array}{r} 0.0 \\ 1.1 \\ 0.1 \\ 5.1 \end{array}\right] $$

Part (d): Finding the size and value of array \(1([1 3], \text{end})\)

To find the array \(1([1 3], \text{end})\), first, we need to understand brackets and the 'end' notation. Brackets specify the indices of the rows we want to extract, and 'end' means the last column of the array. In this case, we want the 1st and 3rd rows and the last column (5th column). The sub-array will have the following elements: $$ \left[\begin{array}{r} 6.0 \\ 1.3 \end{array}\right] $$ Size of array \(1([1 3], \text{end})\): 2 x 1 Value of array \(1([1 3], \text{end})\): $$ \left[\begin{array}{r} 6.0 \\ 1.3 \end{array}\right] $$

Key concepts

Array Size Determination

When working with arrays in MATLAB, understanding their dimensions is crucial. The array size is described by the number of rows and columns it contains. To determine the size of an array, simply count the number of rows and columns it has. For example, considering the array provided:
- There are 4 rows and 5 columns. - Thus, the size of this array is 4 x 5.
This size tells us the shape of the array, which is important when performing operations that rely on conformability or compatibility between arrays.

Matrix Indexing

In MATLAB, accessing specific elements within a matrix or array is done through indexing. This involves specifying the row number followed by the column number in parentheses. For instance, when you see:
- Array1(4, 2), you should look at the 4th row and 2nd column.
The value found here is 5.1, as detailed in the solution. This precise method of indexing allows you to access or modify any particular element within an array, making it an incredibly useful tool in data manipulation and computations.

Colon and End Notation

The colon (":") and end notation in MATLAB are two powerful tools that enhance array operations. The colon is used to represent entire rows or columns, while "end" refers to the last element in a given dimension.

• For example, to extract an entire column, you might use syntax array1(:, 2:2), which gets all the rows in the 2nd column.
• This gives a column vector of size 4 x 1 since every row of the 2nd column is selected.

Similarly, using square brackets along with "end," such as in array1([1 3], end), helps retrieve specific rows and the last column. Here, it selects the 1st and 3rd rows of the last column, resulting in a sub-array. This notation is indispensable for handling larger and more complex data structures, offering both simplicity and depth in array manipulation.