If `U=["2 -3 4"],V=[(3),(2),(1)],X=["0 2 3"]andY=[(2),(2),(4)]`, then find `UV+XY`

Answer

To solve the problem, we need to find the value of \( UV + XY \) where:

- \( U = [2, -3, 4] \) (a row matrix)
- \( V = \begin{bmatrix} 3 \\ 2 \\ 1 \end{bmatrix} \) (a column matrix)
- \( X = [0, 2, 3] \) (a row matrix)
- \( Y = \begin{bmatrix} 2 \\ 2 \\ 4 \end{bmatrix} \) (a column matrix)

### Step 1: Calculate \( UV \)

To calculate \( UV \), we perform the matrix multiplication of \( U \) and \( V \):

\[ UV = [2, -3, 4] \begin{bmatrix} 3 \\ 2 \\ 1 \end{bmatrix} \]

Using the formula for matrix multiplication, we compute:

\[ UV = 2 \cdot 3 + (-3) \cdot 2 + 4 \cdot 1 \]

Calculating each term:

- \( 2 \cdot 3 = 6 \)
- \( -3 \cdot 2 = -6 \)
- \( 4 \cdot 1 = 4 \)

Now, summing these results:

\[ UV = 6 - 6 + 4 = 4 \]

### Step 2: Calculate \( XY \)

Next, we calculate \( XY \):

\[ XY = [0, 2, 3] \begin{bmatrix} 2 \\ 2 \\ 4 \end{bmatrix} \]

Again, using the matrix multiplication formula:

\[ XY = 0 \cdot 2 + 2 \cdot 2 + 3 \cdot 4 \]

Calculating each term:

- \( 0 \cdot 2 = 0 \)
- \( 2 \cdot 2 = 4 \)
- \( 3 \cdot 4 = 12 \)

Now, summing these results:

\[ XY = 0 + 4 + 12 = 16 \]

### Step 3: Calculate \( UV + XY \)

Now that we have both \( UV \) and \( XY \), we can find \( UV + XY \):

\[ UV + XY = 4 + 16 = 20 \]

### Final Answer

Thus, the final result is:

\[ UV + XY = 20 \]