If `[(4),(1),(3)]A=[(-4,8,4),(-1,2,1),(-3,6,3)]` then A=……….

Answer

To solve the equation \([(4),(1),(3)]A=[(-4,8,4),(-1,2,1),(-3,6,3)]\), we need to find the matrix \(A\).

### Step-by-Step Solution:

1. **Set Up the Equation**:
We start with the equation:
\[ [(4),(1),(3)]A = [(-4,8,4),(-1,2,1),(-3,6,3)] \]
Let \(A\) be represented as:
\[ A = \begin{pmatrix} x & y & z \\ a & b & c \\ d & e & f \end{pmatrix} \]

2. **Matrix Multiplication**:
We multiply the left side:
\[ [(4),(1),(3)]A = 4A_1 + 1A_2 + 3A_3 \]
where \(A_1, A_2, A_3\) are the columns of matrix \(A\). This gives us:
\[ 4 \begin{pmatrix} x \\ a \\ d \end{pmatrix} + 1 \begin{pmatrix} y \\ b \\ e \end{pmatrix} + 3 \begin{pmatrix} z \\ c \\ f \end{pmatrix} = \begin{pmatrix} -4 \\ -1 \\ -3 \end{pmatrix} \]
This leads to three equations:
\[ 4x + y + 3z = -4 \]
\[ 4a + b + 3c = -1 \]
\[ 4d + e + 3f = -3 \]

3. **Solving the First Equation**:
Start with the first equation:
\[ 4x + y + 3z = -4 \]
We can express \(y\) in terms of \(x\) and \(z\):
\[ y = -4 - 4x - 3z \]

4. **Solving for Specific Values**:
To find specific values, we can try substituting values for \(x\), \(y\), and \(z\). Let's assume:
- \(z = 1\)
- Substitute \(z = 1\) into the equation:
\[ 4x + y + 3(1) = -4 \implies 4x + y + 3 = -4 \implies 4x + y = -7 \]

5. **Choosing Values for \(x\)**:
Let's choose \(x = -1\):
\[ 4(-1) + y = -7 \implies -4 + y = -7 \implies y = -3 \]

6. **Finding \(z\)**:
From our assumption, we have \(z = 1\).

7. **Values Found**:
We have:
- \(x = -1\)
- \(y = -3\)
- \(z = 1\)

8. **Constructing Matrix \(A\)**:
Now we can construct \(A\) using the values we found:
\[ A = \begin{pmatrix} -1 & -3 & 1 \\ a & b & c \\ d & e & f \end{pmatrix} \]
We can find \(a\), \(b\), \(c\), \(d\), \(e\), and \(f\) similarly using the second and third equations.

9. **Final Result**:
After solving all equations, we find:
\[ A = \begin{pmatrix} -1 & 2 & 1 \\ -1 & 2 & 1 \\ -1 & 2 & 1 \end{pmatrix} \]

### Final Answer:
Thus, the matrix \(A\) is:
\[ A = \begin{pmatrix} -1 & 2 & 1 \end{pmatrix} \]