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

Step 1: Write the given vectors and the equation. 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 $2a + b = c$.

Step 2: Substitute the vectors into the equation. $2 \begin{pmatrix} 2 \\ 3 \end{pmatrix} + \begin{pmatrix} X \\ -3 \end{pmatrix} = \begin{pmatrix} 7 \\ 3 \end{pmatrix}$

Step 3: Perform the scalar multiplication and vector addition. 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: $\begin{pmatrix} 4 + X \\ 6 + (-3) \end{pmatrix} = \begin{pmatrix} 7 \\ 3 \end{pmatrix}$ $\begin{pmatrix} 4 + X \\ 3 \end{pmatrix} = \begin{pmatrix} 7 \\ 3 \end{pmatrix}$

Step 4: Equate the corresponding components to solve for $X$. 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 $3$. $X = 3$ Send me the next one 📸