https://file.aiquickdraw.com/mathbot/file/1729643778764y7aw5cih.jpg

kerjakan secara tabel matriks tolong dengan benar

Let's solve the problem in the image step by step using matrix operations.

We are given the matrix equation:

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

### Step 1: Perform the addition of the matrices on the left-hand side.

The addition of two matrices is done by adding corresponding elements from both matrices. So,

\[
\begin{pmatrix} -1 + 4 & d + (-5) \\ (-b) + 3 & 3 + b \end{pmatrix}
= \begin{pmatrix} 3 & d - 5 \\ -b + 3 & 3 + b \end{pmatrix}
\]

### Step 2: Compare the resulting matrix with the right-hand side matrix.

Now compare the matrix:

\[
\begin{pmatrix} 3 & d - 5 \\ -b + 3 & 3 + b \end{pmatrix}
\]

with the right-hand side matrix:

\[
\begin{pmatrix} 2 & -1 \\ -4 & 3 \end{pmatrix}
\]

This gives us a system of equations by comparing corresponding elements:

1. \( 3 = 2 \) (which is clearly incorrect, so this doesn't provide new information)
2. \( d - 5 = -1 \)
3. \( -b + 3 = -4 \)
4. \( 3 + b = 3 \)

### Step 3: Solve the system of equations.

From equation 2:

\[
d - 5 = -1 \implies d = -1 + 5 = 4
\]

From equation 3:

\[
-b + 3 = -4 \implies -b = -4 - 3 = -7 \implies b = 7
\]

From equation 4:

\[
3 + b = 3 \implies b = 0
\]

So, \( b = 0 \).

However, if \( b = 7 \) from equation 3, this is inconsistent with equation 4. Therefore, there seems to be a contradiction in the problem, which may suggest an error in the given matrices.

Let me know if you'd like further clarification on this!

Jika matriks \[ \begin{pmatrix} -1 & d \\ -b & 3 \end{pmatrix} + \begin{pmatrix} 4 & -5 \\ 3 & b \end{pmatrix} = \begin{pmatrix} 2 & -1 \\ -4 & 3 \end{pmatrix} \], tentukan nilai d.

Learn how to solve a matrix addition problem involving matrix equality to find the value of d. This problem involves key mathematical concepts such as matrix addition and the matrix equality theorem, suitable for students in Grades 10-12.

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