Question
3. \( \left[\begin{array}{cc}1 & -2 \\ 3 & 4\end{array}\right] \times\left[\begin{array}{cc}0 & 2 \\ 1 & -1\end{array}\right] \)
Ask by Barber Schmidt. in Thailand
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The product of the matrices is:
\[
\begin{bmatrix}
-2 & 4 \\
4 & 2
\end{bmatrix}
\]
Solution
It seems there was an error in the calculation. Let's try again.
To calculate the product of two matrices, we need to follow the rules of matrix multiplication. The product of two matrices A and B is a matrix C, where each element of C is the dot product of a row of A and a column of B.
Let's calculate the product of the given matrices step by step:
1. Multiply the first row of the first matrix by the first column of the second matrix:
\(1 \times 0 + (-2) \times 1 = -2\)
2. Multiply the first row of the first matrix by the second column of the second matrix:
\(1 \times 2 + (-2) \times (-1) = 4\)
3. Multiply the second row of the first matrix by the first column of the second matrix:
\(3 \times 0 + 4 \times 1 = 4\)
4. Multiply the second row of the first matrix by the second column of the second matrix:
\(3 \times 2 + 4 \times (-1) = 2\)
Therefore, the product of the given matrices is:
\[
\begin{bmatrix}
-2 & 4 \\
4 & 2
\end{bmatrix}
\]
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Simplify this solution The Deep Dive
To multiply the two matrices \( A = \left[\begin{array}{cc}1 & -2 \\ 3 & 4\end{array}\right] \) and \( B = \left[\begin{array}{cc}0 & 2 \\ 1 & -1\end{array}\right] \), we perform matrix multiplication. The resulting matrix \( C = A \times B \) is calculated as follows: \[ C_{11} = (1 \cdot 0) + (-2 \cdot 1) = 0 - 2 = -2 \] \[ C_{12} = (1 \cdot 2) + (-2 \cdot -1) = 2 + 2 = 4 \] \[ C_{21} = (3 \cdot 0) + (4 \cdot 1) = 0 + 4 = 4 \] \[ C_{22} = (3 \cdot 2) + (4 \cdot -1) = 6 - 4 = 2 \] Thus, the resulting matrix is: \[ \left[\begin{array}{cc}-2 & 4 \\ 4 & 2\end{array}\right] \]
