# arrow_back Why is $|c| ||y|| = ||cy||$ where $y$ is a vector and $c$ is a constant?

11 views
Why is $|c| ||y|| = ||cy||$ where $y$ is a vector and $c$ is a constant?

$|| cy || =\sqrt{(c\cdot y_1)^2+(c\cdot y_2)^2+...+(c\cdot y_n)^2}$

$=\sqrt{c^2\cdot (y_1^2+y_2^2+...+(y_n)^2)}$

$=c\cdot \sqrt{y_1^2+y_2^2+...+(y_n)^2}$

$=|c| ||y||$
by Platinum
(104,456 points)

## Related questions

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Show that $$\| x + y \| \geq | \| x | | - \| y \| |$$
0 answers 44 views
Show that $$\| x + y \| \geq | \| x | | - \| y \| |$$Show that $$&nbsp;&nbsp;\| x + y \| \geq | \| x | | - \| y \| | &nbsp;&nbsp;&nbsp;$$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Find the norm of $v$, and a unit vector that is oppositely directed to $\mathbf{v} = (2, 2, 2)$
0 answers 12 views
Find the norm of $v$, and a unit vector that is oppositely directed to $\mathbf{v} = (2, 2, 2)$Find the norm of $v$, and a unit vector that is oppositely directed to $\mathbf{v} = (2, 2, 2)$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Find the norm of $v$, and a unit vector that is oppositely directed to $\mathbf{v} = (1, -1, 2)$
0 answers 11 views
Find the norm of $v$, and a unit vector that is oppositely directed to $\mathbf{v} = (1, -1, 2)$Find the norm of $v$, and a unit vector that is oppositely directed to $\mathbf{v} = (1, -1, 2)$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
If $\mathbf{v}$ is a vector in $R^{n}$, and if $k$ is any scalar, then prove that $\|k \mathbf{v}\|=|k|\|\mathbf{v}\|$
1 answer 10 views
If $\mathbf{v}$ is a vector in $R^{n}$, and if $k$ is any scalar, then prove that $\|k \mathbf{v}\|=|k|\|\mathbf{v}\|$If $\mathbf{v}$ is a vector in $R^{n}$, and if $k$ is any scalar, then prove that $\|k \mathbf{v}\|=|k|\|\mathbf{v}\|$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Find a unit vector that is orthogonal to both $\mathbf{u}=(1,0,1)$ and $\mathbf{v}=(0,1,1)$
0 answers 6 views
Find a unit vector that is orthogonal to both $\mathbf{u}=(1,0,1)$ and $\mathbf{v}=(0,1,1)$Find a unit vector that is orthogonal to both $\mathbf{u}=(1,0,1)$ and $\mathbf{v}=(0,1,1)$ ...
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 norm of a vector?
1 answer 208 views
What is the norm of a vector?What is the norm of a vector? ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Normalize the vector $v=(1,-3,4,2)$
1 answer 99 views
Normalize the vector $v=(1,-3,4,2)$Normalize the vector $v=(1,-3,4,2)$ ...
close