# arrow_back Let $\mathbf{u}$ be a vector in $R^{100}$ whose $i$ th component is $i$, and let $\mathbf{v}$ be the vector in $R^{100}$ whose $i$ th component is $1 /(i+1)$. Find the dot product of $\mathbf{u}$ and $\mathbf{v}$.

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Let $\mathbf{u}$ be a vector in $R^{100}$ whose $i$ th component is $i$, and let $\mathbf{v}$ be the vector in $R^{100}$ whose $i$ th component is $1 /(i+1)$. Find the dot product of $\mathbf{u}$ and $\mathbf{v}$.

What is the dot product of $\mathbf{u}$ a column matrix and $\mathbf{v}$ a column matrix?
What is the dot product of $\mathbf{u}$ a column matrix and $\mathbf{v}$ a column matrix?What is the dot product of $\mathbf{u}$ a column matrix and $\mathbf{v}$ a column matrix? ...
Prove that if $\mathbf{u}$ and $\mathbf{v}$ are vectors in $R^{n}$ with the Euclidean inner product, then $$\mathbf{u} \cdot \mathbf{v}=\frac{1}{4}\|\mathbf{u}+\mathbf{v}\|^{2}-\frac{1}{4}\|\mathbf{u}-\mathbf{v}\|^{2}$$Prove that if $\mathbf{u}$ and $\mathbf{v}$ are vectors in $R^{n}$ with the Euclidean inner product, then $$\mathbf{u} \cdot \mathbf{v}=\frac{1}{4}\| ... close 0 answers 11 views close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the dot product of u a row matrix and v a column matrix? 1 answer 13 views What is the dot product of u a row matrix and v a column matrix?What is the dot product of u a row matrix and v a column matrix? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the dot product of u a column matrix and v a row matrix? 1 answer 13 views What is the dot product of u a column matrix and v a row matrix?What is the dot product of u a column matrix and v a row matrix? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the dot product of u a row matrix and v a row matrix? 1 answer 9 views What is the dot product of u a row matrix and v a row matrix?What is the dot product of u a row matrix and v a row matrix? ... close 1 answer 12 views If \mathbf{u} and \mathbf{v} are orthogonal vectors in R^{n} with the Euclidean inner product, then prove that$$ \|\mathbf{u}+\mathbf{v}\|^{2}=\|\mathbf{u}\|^{2}+\|\mathbf{v}\|^{2} $$If \mathbf{u} and \mathbf{v} are orthogonal vectors in R^{n} with the Euclidean inner product, then prove that$$ \|\mathbf{u}+\mathbf{v}\|^{2}= ...