Recent content by TsAmE

Homework Statement Determine if the system y(t) = sin(x(t)) is time invariant, linear, causal, and/or memoryless. Homework Equations None. The Attempt at a Solution The system is time invariant and is non-linear, but I don't understand why it is causal and has memory.

It would then go to X. So if there is no current through a resistor, would the resistor be treated as an ideal wire (with no resistance) and thus the same voltage as the line?

Homework Statement Calculate the current i and the voltage appearing at X and Y Homework Equations None. The Attempt at a Solution I found I to be 0.002A and Vy = 2V, but I am having trouble with Vx Attempt: I tried getting the current that goes through the 3k and 4k...

Oh I see. Would this be right? \mathbf{Ax_1} = \mathbf{b} \mathbf{AR_1x_1} = \mathbf{bR_1} \mathbf{I_2x_1} = \mathbf{bR_1} \mathbf{x_1} = \mathbf{bR_1} and the same calculations for \mathbf{x_2}?

Homework Statement Show that \mathbf{R_1} = \begin{pmatrix}-1 & 1 \\ 6& -4 \\ 4& -3\end{pmatrix} and \mathbf{R_2} = \begin{pmatrix}1 & -1 \\ -4& 6 \\ -4& 5\end{pmatrix} are both right-inverses of the matrix \mathbf{A} = \begin{pmatrix}1 &1 &-1 \\ 4&0 &1 \end{pmatrix}. Use the...

Homework Statement How would you find a vector perpendicular to (2,-1,1)? Homework Equations None. The Attempt at a Solution I tried saying (x,y,z) x (2,-1,1) = 1 (since sin90 max at 1) but have 3 unknowns, x, y and z so don't know how to get a numerical answer

Dont you mean I have this parametrization of the plane: \begin{pmatrix}x\\y \\z\end{pmatrix} = \begin{pmatrix}\frac{-5}{2}\\0 \\0\end{pmatrix} + \lambda \begin{pmatrix}\frac{5}{2}\\1\\0\end{pmatrix} + \mu\begin{pmatrix}-1\\0 \\1\end{pmatrix} corresponding to: x = \frac{-5}{2} +...

Nevermind, I found what I did wrong :smile:. For the second part of the question it asked: To which point does the matrix A take the point P(1,4)? Attempt: \begin{pmatrix}\frac{1}{\sqrt{2}} & 0 & \\ -\frac{1}{\sqrt{2}} & 0 & \end{pmatrix} \begin{pmatrix}1 & 0 & \\ 0 &4&\end{pmatrix}...

Homework Statement Find the 2 x 2 matrix A which represents a projection onto the x-axis, followed by a clockwise rotation through pi/4. Homework Equations None The Attempt at a Solution \begin{pmatrix} cos\frac{\pi}{4}&sin\frac{\pi}{4} \\...

I tried checking the x values so I subbed x = 1 into x = \frac{-5}{2} + \frac{5}{2}\lambda - \mu and got x = -1 and for \begin{pmatrix}x\\y \\z\end{pmatrix} = \begin{pmatrix}1\\3 \\4\end{pmatrix} + \lambda \begin{pmatrix}5\\2\\0\end{pmatrix} + \mu\begin{pmatrix}1\\0 \\-1\end{pmatrix} I got x =...

I see, but where did I go wrong with the vector with the parametric representation of the plane, cause I can't see what I did wrong.

Homework Statement Let T: \mathbb{R}^3 \to \mathbb{R}^3 be the linear map represented by the matrix \begin{pmatrix} 4 & -1 & 0 \\ 6& 3 & -2\\ 12& 6 & -4\end{pmatrix} What is the image under T of the plane 2x - 5y + 2z = -5? Homework Equations None The Attempt at a Solution I...

Forgot to add the diagram

Homework Statement What is the minimum input voltage for which the transistor will begin to turn on? Homework Equations None. The Attempt at a Solution I don't understand why the answer was 0.7V. I understand that yes by the time you reach the base there will be 0.7V left which...