Solve for a,b and c, if,
(i) `[{:(,-4,a+5),(,3,2):}]=[{:(,b+4,2),(,3,c-1):}]`
(ii) `[{:(,a,a-b),(,b+c,0):}]=[{:(,3,-1),(,2,0):}]`

Answer

To solve for \( a \), \( b \), and \( c \) in the given matrix equations, we will break down the problem step by step.

### Part (i)

We have the equation:

\[ \begin{pmatrix} -4 & a + 5 \\ 3 & 2 \end{pmatrix} = \begin{pmatrix} b + 4 & 2 \\ 3 & c - 1 \end{pmatrix} \]

From this equation, we can equate the corresponding elements of the matrices.

1. **Equate the first element:**
\[ -4 = b + 4 \]
To find \( b \), we solve for \( b \):
\[ b = -4 - 4 = -8 \]

2. **Equate the second element of the first row:**
\[ a + 5 = 2 \]
To find \( a \), we solve for \( a \):
\[ a = 2 - 5 = -3 \]

3. **Equate the second element of the second row:**
\[ 2 = c - 1 \]
To find \( c \), we solve for \( c \):
\[ c = 2 + 1 = 3 \]

Thus, from part (i), we have:
\[ a = -3, \quad b = -8, \quad c = 3 \]

### Part (ii)

We have the equation:

\[ \begin{pmatrix} a & a - b \\ b + c & 0 \end{pmatrix} = \begin{pmatrix} 3 & -1 \\ 2 & 0 \end{pmatrix} \]

Again, we equate the corresponding elements of the matrices.

1. **Equate the first element:**
\[ a = 3 \]

2. **Equate the second element of the first row:**
\[ a - b = -1 \]
Substituting \( a = 3 \):
\[ 3 - b = -1 \]
Solving for \( b \):
\[ -b = -1 - 3 \implies -b = -4 \implies b = 4 \]

3. **Equate the first element of the second row:**
\[ b + c = 2 \]
Substituting \( b = 4 \):
\[ 4 + c = 2 \]
Solving for \( c \):
\[ c = 2 - 4 = -2 \]

Thus, from part (ii), we have:
\[ a = 3, \quad b = 4, \quad c = -2 \]

### Final Results

Combining results from both parts, we have:
- From part (i): \( a = -3, b = -8, c = 3 \)
- From part (ii): \( a = 3, b = 4, c = -2 \)