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Problem 10

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

Expert verified
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'.
See the step by step solution

## 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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