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Problem 1

# Refer to the following matrices: $A=\left[\begin{array}{rrrr}2 & -3 & 9 & -4 \\ -11 & 2 & 6 & 7 \\ 6 & 0 & 2 & 9 \\ 5 & 1 & 5 & -8\end{array}\right]$ $B=\left[\begin{array}{rrr}3 & -1 & 2 \\ 0 & 1 & 4 \\ 3 & 2 & 1 \\ -1 & 0 & 8\end{array}\right]$ $$C=\left[\begin{array}{lllll}1 & 0 & 3 & 4 & 5\end{array}\right]$$ $$D=\left[\begin{array}{r}1 \\ 3 \\ -2 \\ 0\end{array}\right]$$ What is the size of $$A ?$$ Of $$B ?$$ Of $$C$$ ? Of $$D ?$$

Expert verified
The sizes of the given matrices are: $$A: 4\times4$$, $$B: 4\times3$$, $$C: 1\times5$$, and $$D: 4\times1$$.
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## Step 1: Size of Matrix A

The size of a matrix is given by the number of rows followed by the number of columns. In matrix A, there are 4 rows and 4 columns. Thus, the size of A is 4x4.

## Step 2: Size of Matrix B

Count the number of rows and columns in matrix B. There are 4 rows and 3 columns, so the size of B is 4x3.

## Step 3: Size of Matrix C

Observing matrix C, we see that it has only 1 row and 5 columns. Therefore, the size of C is 1x5.

## Step 4: Size of Matrix D

Lastly, matrix D contains 4 rows and 1 column, giving it a size of 4x1. To summarize: 1. The size of matrix A is 4x4. 2. The size of matrix B is 4x3. 3. The size of matrix C is 1x5. 4. The size of matrix D is 4x1.

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