Let's solve the matrix multiplication problem shown in the image step by step.
We are multiplying two
2×2 matrices:
$$
\begin{bmatrix}
0 & 2 \\
-2 & -5
\end{bmatrix}
\cdot
\begin{bmatrix}
6 & -6 \\
3 & 0
\end{bmatrix}
$$
---
🔹 Matrix Multiplication Rule:
To multiply two matrices, we take the
dot product of the rows of the first matrix with the columns of the second matrix.
The result will be a
2×2 matrix.
Let’s compute each element of the resulting matrix.
---
Step 1: First row, first column (R1C1)
Take the first row of the first matrix: $[0, 2]$
Take the first column of the second matrix: $[6, 3]$
$$
(0)(6) + (2)(3) = 0 + 6 = 6
$$
---
Step 2: First row, second column (R1C2)
First row: $[0, 2]$
Second column: $[-6, 0]$
$$
(0)(-6) + (2)(0) = 0 + 0 = 0
$$
---
Step 3: Second row, first column (R2C1)
Second row: $[-2, -5]$
First column: $[6, 3]$
$$
(-2)(6) + (-5)(3) = -12 - 15 = -27
$$
---
Step 4: Second row, second column (R2C2)
Second row: $[-2, -5]$
Second column: $[-6, 0]$
$$
(-2)(-6) + (-5)(0) = 12 + 0 = 12
$$
---
✔ Final Result:
$$
\begin{bmatrix}
6 & 0 \\
-27 & 12
\end{bmatrix}
$$
---
🟩 Answer:
$$
\boxed{
\begin{bmatrix}
6 & 0 \\
-27 & 12
\end{bmatrix}
}
$$
This is the correct result of the matrix multiplication.
Parent Tip: Review the logic above to help your child master the concept of algebra 2 matrix worksheet.
