if A=`diag [1" "3" "4],B="diag"[-2" "1" "-1],C="Diag"[3" "-1" "-2]`then find 2A +B-C.

Explanation

To solve the problem, we need to find the expression \(2A + B - C\) given the matrices \(A\), \(B\), and \(C\).

1. **Define the matrices:**
- Matrix \(A = \text{diag}(1, 3, 4)\)
- Matrix \(B = \text{diag}(-2, 1, -1)\)
- Matrix \(C = \text{diag}(3, -1, -2)\)

2. **Write the matrices in matrix form:**
- \(A = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{pmatrix}\)
- \(B = \begin{pmatrix} -2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1 \end{pmatrix}\)
- \(C = \begin{pmatrix} 3 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -2 \end{pmatrix}\)

3. **Calculate \(2A\):**
\[ 2A = 2 \times \begin{pmatrix} 1 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{pmatrix} = \begin{pmatrix} 2 & 0 & 0 \\ 0 & 6 & 0 \\ 0 & 0 & 8 \end{pmatrix} \]

4. **Add \(2A\) and \(B\):**
\[ 2A + B = \begin{pmatrix} 2 & 0 & 0 \\ 0 & 6 & 0 \\ 0 & 0 & 8 \end{pmatrix} + \begin{pmatrix} -2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1 \end{pmatrix} = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 7 & 0 \\ 0 & 0 & 7 \end{pmatrix} \]

5. **Subtract \(C\) from the result:**
\[ 2A + B - C = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 7 & 0 \\ 0 & 0 & 7 \end{pmatrix} - \begin{pmatrix} 3 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -2 \end{pmatrix} = \begin{pmatrix} -3 & 0 & 0 \\ 0 & 8 & 0 \\ 0 & 0 & 9 \end{pmatrix} \]

6. **Final Result:**
The final result is:
\[ 2A + B - C = \text{diag}(-3, 8, 9) \]