Question

3. Consider a linear system whose augmented matrix is of the form $\begin{pmatrix} 1 & 2 & 1 & \vert & 0\\ 2 & 5 & 3 & \vert & 0\\ -1 & 1 & \beta & \vert & 0 \end{pmatrix}$ a) Is it possible for the system to be inconsistent? Explain. b) For what values of $\beta$ will the system have infinitely many solutions?

          3. Consider a linear system whose augmented matrix is of the form
$\begin{pmatrix} 1 & 2 & 1 & \vert & 0\\ 2 & 5 & 3 & \vert & 0\\ -1 & 1 & \beta & \vert & 0 \end{pmatrix}$
a) Is it possible for the system to be inconsistent? Explain.
b) For what values of $\beta$ will the system have infinitely many solutions?

3. Consider a linear system whose augmented matrix is of the form
< p m a t r i x >
a) Is it possible for the system to be inconsistent? Explain.
b) For what values of β will the system have infinitely many solutions?

Added by Nicole B.

Principles of Economics

Gregory Mankiw 8th Edition

Instant Answer

Solved by Expert Akash M

Step 1

This can happen if there is a row in the augmented matrix that has all zeros except for the last column, which contains a non-zero value. In this case, the last equation would be something like 0x + 0y + 0z + ... + 0n = k, where k is a non-zero constant. This Show more…

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3. Consider a linear system whose augmented matrix is of the form aIs it possible for the system to be inconsistent? Explain. b For what values of will the system have infinitely many solutions?