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Write down the given vector equation.

May 7, 2026Mathematics

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\begin{pmatrix} -2 \\ 4 \end{pmatrix}

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Write down the given vector equation.
We are given the vectors $R = \begin{pmatrix} -4 \\ 9 \end{pmatrix}$ , $U = \begin{pmatrix} x \\ y \end{pmatrix}$ , and their sum $U + R = \begin{pmatrix} -6 \\ 13 \end{pmatrix}$ .
Substitute the expressions for $U$ and $R$ into the sum equation.
$\begin{pmatrix} x \\ y \end{pmatrix} + \begin{pmatrix} -4 \\ 9 \end{pmatrix} = \begin{pmatrix} -6 \\ 13 \end{pmatrix}$
Perform the vector addition on the left side.
$\begin{pmatrix} x + (-4) \\ y + 9 \end{pmatrix} = \begin{pmatrix} -6 \\ 13 \end{pmatrix}$ $\begin{pmatrix} x - 4 \\ y + 9 \end{pmatrix} = \begin{pmatrix} -6 \\ 13 \end{pmatrix}$
Equate the corresponding components to form two separate equations.
For the x-component:
$x - 4 = -6$
For the y-component:
$y + 9 = 13$
Solve each equation for $x$ and $y$ .
For $x$ :
$x - 4 = -6$ $x = -6 + 4$ $x = -2$
For $y$ :
$y + 9 = 13$ $y = 13 - 9$ $y = 4$
State the components of vector $U$ .
The components of $U$ are $x = -2$ and $y = 4$ .
So, $U = \begin{pmatrix} -2 \\ 4 \end{pmatrix}$ .

The component of U is $\begin{pmatrix} -2 \\ 4 \end{pmatrix}$ .

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