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Single choice
Question at position 12 [1−134][025−3]=\begin{bmatrix} 1 & -1 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} 0 & 2 \\ 5 & -3 \end{bmatrix} =[−5520−6]\begin{bmatrix} -5 & 5 \\ 20 & -6 \end{bmatrix}[68−4−17]\begin{bmatrix} 6 & 8 \\ -4 & -17 \end{bmatrix}[−2838]\begin{bmatrix} -2 & 8 \\ 3 & 8 \end{bmatrix}[4−106]\begin{bmatrix} 4 & -1 \\ 0 & 6 \end{bmatrix}[0−215−12]\begin{bmatrix} 0 & -2 \\ 15 & -12 \end{bmatrix}
Options
A.[
−
5
5
20
−
6
]
B.[
6
8
−
4
−
17
]
C.[
−
2
8
3
8
]
D.[
4
−
1
0
6
]
E.[
0
−
2
15
−
12
]
View Explanation
Verified Answer
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Step-by-Step Analysis
To tackle this problem, I will restate the given sequence and then examine each candidate option in turn, explaining what each represents and why it does or does not match.
- The question begins with a chain of matrix multiplications: (1 -1; 3 4) times (0 2; 5 -3) equals something. When you multiply the two 2x2 matrices, you compute each entry of the product:
- Top-left entry: 1*0 + (-1)*5 = -5
- Top-right entry: 1*2 + (-1)*(-3) = 2 + 3 = 5
- Bottom-left entry: 3*0 + 4*5 = 0 + 20 = 20
- Bottom-right entry: 3*2 + 4*(-3) = 6 - 12 = -6
So the product is the 2x2 matrix [ [-5, 5], ......Login to view full explanationLog in for full answers
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