- #1

karush

Gold Member

MHB

- 3,269

- 5

$

v=\left[\begin{array}{r}

-3\\-4\\-5\\4\\-1

\end{array}\right]

w=\left[\begin{array}{r}

-2\\0 \\1 \\4 \\-1

\end{array}\right]

x=\left[\begin{array}{r}

2\\3 \\4 \\-5 \\0

\end{array}\right]

y=\left[\begin{array}{r}

-2\\1 \\0 \\-2 \\7

\end{array}\right]

z=\left[\begin{array}{r}

-1\\0 \\2 \\-3 \\5

\end{array}\right]

$

Construct matrices not yet row reduced echelon form whose null space consists all linear combinations of

1. just x

2. just y

3. just z

ok I presume this

$A_1=a_1\left[\begin{array}{r}2\\3 \\4 \\-5 \\0\end{array}\right]

=\left[\begin{array}{r}2a_1\\3a_1 \\4a_1 \\-5a_1 \\0\end{array}\right]

$

v=\left[\begin{array}{r}

-3\\-4\\-5\\4\\-1

\end{array}\right]

w=\left[\begin{array}{r}

-2\\0 \\1 \\4 \\-1

\end{array}\right]

x=\left[\begin{array}{r}

2\\3 \\4 \\-5 \\0

\end{array}\right]

y=\left[\begin{array}{r}

-2\\1 \\0 \\-2 \\7

\end{array}\right]

z=\left[\begin{array}{r}

-1\\0 \\2 \\-3 \\5

\end{array}\right]

$

Construct matrices not yet row reduced echelon form whose null space consists all linear combinations of

1. just x

2. just y

3. just z

ok I presume this

$A_1=a_1\left[\begin{array}{r}2\\3 \\4 \\-5 \\0\end{array}\right]

=\left[\begin{array}{r}2a_1\\3a_1 \\4a_1 \\-5a_1 \\0\end{array}\right]

$

Last edited: