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3 years ago

Extra Credits:

Mathematics

1 answer:

Effectus [21]3 years ago

8 0

Answer:

Missing Number) 55

Property being used) Distributive

Step-by-step explanation:

To find the missing number, just plug in reasonable numbers from the other equation. It is distributive because the 55 is being distributed into everything that is inside the parentheses. If you need more help, comment and I'll be more than glad to assist you! :P

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babunello [35]

Let $\mathbf V$ be the $m\times3$ matrix whose columns are $\mathbf v_1,\mathbf v_2,\mathbf v_3$ , and let $\mathbf c$ be the vector whose components are the constants $c_1,c_2,c_3$ . Now consider the matrix equation

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More explicitly, we're writing

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$\mathbf V^\top\mathbf V=\begin{bmatrix}{\mathbf v_1}^\top\\{\mathbf v_2}^\top\\{\mathbf v_3}^\top\end{bmatrix}\begin{bmatrix}\mathbf v_1&\mathbf v_2&\mathbf v_3\end{bmatrix}=\begin{bmatrix}{\mathbf v_1}^\top\mathbf v_1&{\mathbf v_1}^\top\mathbf v_2&{\mathbf v_1}^\top\mathbf v_3\\{\mathbf v_2}^\top\mathbf v_1&{\mathbf v_2}^\top\mathbf v_2&{\mathbf v_2}^\top\mathbf v_3\\{\mathbf v_3}^\top\mathbf v_1&{\mathbf v_3}^\top\mathbf v_2&{\mathbf v_3}^\top\mathbf v_3\end{bmatrix}$

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$\mathbf V^\top\mathbf V=\begin{bmatrix}\|\mathbf v_1\|^2&0&0\\0&\|\mathbf v_2\|^2&0\\0&0&\|\mathbf v_3\|^2\end{bmatrix}$

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