Let A = begin{bmatrix} 1 & 1 & 1 0 & 1 & 3 | vedclass

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Question

(A) Given the matrix equation $AX = B$: $\begin{bmatrix} 1 & 1 & 1 \ 0 & 1 & 3 \ 1 & -2 & 1 \end{bmatrix} \begin{bmatrix} a \ b \ c \end{bmatrix}

Vedclass · Accepted Answer

$10$

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(A) Given the matrix equation $AX = B$: $\begin{bmatrix} 1 & 1 & 1 \ 0 & 1 & 3 \ 1 & -2 & 1 \end{bmatrix} \begin{bmatrix} a \ b \ c \end{bmatrix} = \begin{bmatrix} 6 \ 11 \ 0 \end{bmatrix}$ This corresponds to the system of linear equations: $1) \quad a + b + c = 6$ $2) \quad b + 3c = 11$ $3) \quad a - 2b + c = 0$ From equation $(3)$,we have $a + c = 2b$. Substitute $a + c = 2b$ into equation $(1)$: $2b + b = 6 \implies 3b = 6 \implies b = 2$. Now,substitute $b = 2$ into equation $(2)$: $2 + 3c = 11 \implies 3c = 9 \implies c = 3$. Finally,substitute $b = 2$ and $c = 3$ into equation $(1)$: $a + 2 + 3 = 6 \implies a + 5 = 6 \implies a = 1$. We need to find the value of $2a + b + 2c$: $2(1) + 2 + 2(3) = 2 + 2 + 6 = 10$.

Let $A = \begin{bmatrix} 1 & 1 & 1 \\ 0 & 1 & 3 \\ 1 & -2 & 1 \end{bmatrix}$,$B = \begin{bmatrix} 6 \\ 11 \\ 0 \end{bmatrix}$ and $X = \begin{bmatrix} a \\ b \\ c \end{bmatrix}$. If $AX = B$,then the value of $2a + b + 2c$ is:

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