44 lines
862 B
Markdown
44 lines
862 B
Markdown
# Review 8-4
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* Hajin Ju, 2024062806
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## Problem 1
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What is the dimension of the matrix product $AB$ if $A$ is a $p\times q$ matrix and $B$ is a $q\times r$ matrix?
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### Solution 1
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$p\times r$
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## Problem 2
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Count the number of scalar multiplications to multiply $A$ and $B$ where $A$ is a $p\times q$ matrix and $B$ is a $q\times r$ matrix.
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### Solution 2
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$pqr$
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## Problem 3
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Count the number of scalar multiplications where the dimensions of $A_1$, $A_2$, and $A_3$ are $10\times 100$, $100\times 5$ and $5\times 50$, respectively.
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1. $(A_1A_2)A_3$
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2. $A_1(A_2A_3)$
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### Solution 3
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1. $5000 + 2500 = 7500$
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2. $25000 + 50000 = 75000$
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## Problem 4
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Fully parenthesize the product $A_1A_2A_3A_4$. (There are five distinct ways.)
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### Solution 4
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1. $(A_1A_2)(A_3A_4)$
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2. $(A_1(A_2A_3))A_4$
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3. $A_1(A_2(A_3A_4))$
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4. $A_1((A_2A_3)A_4)$
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5. $((A_1A_2)A_3)A_4$
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