Row vectors

**skittle** · February 21st 2011, 09:25 AM

v1 = (2 1 1 1)

v2 = (0 1 1 3)

v1 and v2 are column vectors.

If c =(c1 c2 c3 c4) is a row vector (i.e. a 1 by 4 matrix), what equations must be satisfied by c1; c2; c3; c4 in order that cv1 and cv2 both be zero (as 1 by 1 matrices)?

I have no clue how to start, so any help would be great.

**TheEmptySet** · February 21st 2011, 09:48 AM

Originally Posted by skittle

v1 = (2 1 1 1)

v2 = (0 1 1 3)

v1 and v2 are column vectors.

If c =(c1 c2 c3 c4) is a row vector (i.e. a 1 by 4 matrix), what equations must be satisfied by c1; c2; c3; c4 in order that cv1 and cv2 both be zero (as 1 by 1 matrices)?

I have no clue how to start, so any help would be great.

If you insist on writing the problem with the row's and columns as specified then you need to solve this system

$\begin{bmatrix}c_1 & c_2 & c_3 & c_4 \end{bmatrix}\begin{bmatrix} 2 & 0 \\ 1 & 1 \\ 1 & 1 \\ 1 & 3\end{bmatrix}=\begin{bmatrix}0 & 0 \end{bmatrix}$

But if you transpose both sides of the equation you get

$\begin{bmatrix} 2 & 1& 1 & 1 \\ 0 & 1 & 1 & 3\end{bmatrix}\begin{bmatrix} c_1 \\ c_2 \\ c_3 \\ c_4 \end{bmatrix}=\begin{bmatrix} 0 \\ 0\end{bmatrix}$

or as an augmented matrix

$\begin{bmatrix} 2 & 1 & 1& 1 & 0 \\ 0 & 1 & 1 & 3 & 0\end{bmatrix}$

Solving this will give you the relationships.

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