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Chapter 3: Chapter 3

Problem 10

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Find the dimensions of the given matrix and identify the given entry. $$ \left.E=\left[\begin{array}{llll} d & d & d & d \end{array}\right] ; E_{1 r} \text { (any } r\right) $$

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The dimensions of the given matrix \(E = \begin{bmatrix} d & d & d & d \end{bmatrix}\) are 1 x 4 (1 row and 4 columns). The entry \(E_{1r}\) (where \(r\) can be any value between 1 and 4) is always 'd'.
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Determine the dimensions of the matrix.

The given matrix is: $$ E = \begin{bmatrix} d & d & d & d \end{bmatrix} $$ As it consists of a single row and 4 columns, the dimensions are 1 x 4 (1 row and 4 columns).

Step 2: Identify the given entry \(E_{1r}\).

The entry \(E_{1r}\) refers to the element on the first row (since 1 is the row number) and column \(r\). Since the matrix has only 1 row, we can choose any column number \(r \in \{1, 2, 3, 4 \}\). In all cases, the values are 'd'. For example, let's choose \(r=2\): $$ E_{1r} = E_{12} = d $$ So, the dimensions of the given matrix are 1 x 4, and the entry \(E_{1r}\) comes out to be 'd', for any given value of \(r\).

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