Given that a =(2/3) b. = (X /-3) and c=(7/3) find the value of x if 2a +b= c

The vectors are:

$$a = \begin{pmatrix} 2 \\ 3 \end{pmatrix}, \quad b = \begin{pmatrix} X \\ -3 \end{pmatrix}, \quad c = \begin{pmatrix} 7 \\ 3 \end{pmatrix}$$

The given equation is $2a + b = c$.

First, multiply vector $a$ by the scalar 2:

$$\begin{pmatrix} 2 \times 2 \\ 2 \times 3 \end{pmatrix} + \begin{pmatrix} X \\ -3 \end{pmatrix} = \begin{pmatrix} 7 \\ 3 \end{pmatrix}$$ $$\begin{pmatrix} 4 \\ 6 \end{pmatrix} + \begin{pmatrix} X \\ -3 \end{pmatrix} = \begin{pmatrix} 7 \\ 3 \end{pmatrix}$$

Next, add the two vectors on the left side:

$$\begin{pmatrix} 4 + X \\ 6 + (-3) \end{pmatrix} = \begin{pmatrix} 7 \\ 3 \end{pmatrix}$$ $$\begin{pmatrix} 4 + X \\ 3 \end{pmatrix} = \begin{pmatrix} 7 \\ 3 \end{pmatrix}$$

For the vectors to be equal, their corresponding components must be equal.
Equating the first components:

$$4 + X = 7$$

Solve for $X$:

$$X = 7 - 4$$ $$X = 3$$

Equating the second components (to verify, though not needed to find $X$):

$$3 = 3$$

This confirms the calculation.

The value of $X$ is 3.