If `A=[(2,3,1),(3,1,5)],B=[(1,2,-1),(0,-1,3)]` then `2A-3B=`………….

Answer

To solve the problem \(2A - 3B\) where \(A = \begin{pmatrix} 2 & 3 & 1 \\ 3 & 1 & 5 \end{pmatrix}\) and \(B = \begin{pmatrix} 1 & 2 & -1 \\ 0 & -1 & 3 \end{pmatrix}\), we will follow these steps:

### Step 1: Calculate \(2A\)

Multiply each element of matrix \(A\) by 2.

\[ 2A = 2 \times \begin{pmatrix} 2 & 3 & 1 \\ 3 & 1 & 5 \end{pmatrix} = \begin{pmatrix} 2 \times 2 & 2 \times 3 & 2 \times 1 \\ 2 \times 3 & 2 \times 1 & 2 \times 5 \end{pmatrix} = \begin{pmatrix} 4 & 6 & 2 \\ 6 & 2 & 10 \end{pmatrix} \]

### Step 2: Calculate \(3B\)

Multiply each element of matrix \(B\) by 3.

\[ 3B = 3 \times \begin{pmatrix} 1 & 2 & -1 \\ 0 & -1 & 3 \end{pmatrix} = \begin{pmatrix} 3 \times 1 & 3 \times 2 & 3 \times -1 \\ 3 \times 0 & 3 \times -1 & 3 \times 3 \end{pmatrix} = \begin{pmatrix} 3 & 6 & -3 \\ 0 & -3 & 9 \end{pmatrix} \]

### Step 3: Calculate \(2A - 3B\)

Now we will subtract \(3B\) from \(2A\).

\[ 2A - 3B = \begin{pmatrix} 4 & 6 & 2 \\ 6 & 2 & 10 \end{pmatrix} - \begin{pmatrix} 3 & 6 & -3 \\ 0 & -3 & 9 \end{pmatrix} \]

Subtract corresponding elements:

\[ = \begin{pmatrix} 4 - 3 & 6 - 6 & 2 - (-3) \\ 6 - 0 & 2 - (-3) & 10 - 9 \end{pmatrix} \]

Calculating each element:

\[ = \begin{pmatrix} 1 & 0 & 5 \\ 6 & 5 & 1 \end{pmatrix} \]

### Final Answer

Thus, \(2A - 3B = \begin{pmatrix} 1 & 0 & 5 \\ 6 & 5 & 1 \end{pmatrix}\).

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