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Home » J: $eginpmatrix 0 & -1 \ 0 & 1 \endpmatrix$ - ToelettAPP

J: $eginpmatrix 0 & -1 \ 0 & 1 \endpmatrix$ - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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f(2) + f(0) = 4 \quad \text{(1)}
Now plug in $ a = 0, b = 1 $:
f(1) + f(-1) = 2f(0) + 2f(1) \Rightarrow 1 + f(-1) = 2f(0) + 2 \Righta...
Now plug in $ a = 1, b = 0 $:
f(1) + f(1) = 2f(1) + 2f(0) \Rightarrow 2 = 2 + 2f(0) \Rightarrow f(0)...
Substitute $ f(0) = 0 $ into equation (1):
f(2) + 0 = 4 \Rightarrow f(2) = \boxed{4}
Question: Find the area enclosed by the graph of $ |x| + |y| = 4 $.
Solution: The equation $ |x| + |y| = 4 $ represents a diamond (rhombus...
The diamond has diagonals of length 8 (horizontal) and 8 (vertical), s...

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The component of \(\mathbf{v}\) perpendicular to \(\mathbf{c}\) is giv...
\mathbf{v}_{\perp} = \mathbf{v} - ext{proj}_{\mathbf{c}} \mathbf{v}
where
ext{proj}_{\mathbf{c}} \mathbf{v} = \left( rac{\mathbf{v} \cdot \math...
ight) \mathbf{c}
First, compute the dot products:
\mathbf{v} \cdot \mathbf{c} = (2)(1) + (-1)(2) + (3)(-1) = 2 - 2 - 3 =...
\mathbf{c} \cdot \mathbf{c} = 1^2 + 2^2 + (-1)^2 = 1 + 4 + 1 = 6
ext{proj}_{\mathbf{c}} \mathbf{v} = rac{-3}{6} egin{pmatrix} 1 \ 2 \...
Now compute the perpendicular component:

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