(AX=B), x+5y=-10, -2x+7y=-31

Jaylene Hunter
2022-07-26
Answered

Solve the following system of equations by using the inverse of the coefficient matrix A.

(AX=B), x+5y=-10, -2x+7y=-31

(AX=B), x+5y=-10, -2x+7y=-31

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sweetwisdomgw

Answered 2022-07-27
Author has **20** answers

$\left[\begin{array}{cc}1& 5\\ -2& 7\end{array}\right]\left\{\begin{array}{c}x\\ y\end{array}\right\}=\left\{\begin{array}{c}-10\\ -31\end{array}\right\}$

${A}^{-1}=\frac{1}{(1\ast 7)-(5\ast -2)}\left[\begin{array}{cc}7& -5\\ 2& 1\end{array}\right]=\frac{1}{17}\left[\begin{array}{cc}7& -5\\ 2& 1\end{array}\right]$

${A}^{-1}=\frac{1}{(1\ast 7)-(5\ast -2)}\left[\begin{array}{cc}7& -5\\ 2& 1\end{array}\right]=\frac{1}{17}\left[\begin{array}{cc}7& -5\\ 2& 1\end{array}\right]$

asked 2021-06-13

For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A.

$A=\left[\begin{array}{cccc}2& 3& 5& -9\\ -8& -9& -11& 21\\ 4& -3& -17& 27\end{array}\right]$

Find a nonzero vector in Nul A.

$A=\left[\begin{array}{c}-3\\ 2\\ 0\\ 1\end{array}\right]$

Find a nonzero vector in Nul A.

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Find an explicit description of Nul A by listing vectors that span the null space.

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Assume that A is row equivalent to B. Find bases for Nul A and Col A.

asked 2022-06-03

If a nonzero matrix $A$ is transformed from ${\mathbb{R}}^{3}$ to ${\mathbb{R}}^{2}$, then the null space of $A$ must be a one dimensional (sub)space of ${\mathbb{R}}^{3}$.

So i know that null space of $A$ is $\{x:Ax=0\}$ and I also know the definition of not onto. I don't understand the whole concept of one-dimensional space and would this statement be always true?

So i know that null space of $A$ is $\{x:Ax=0\}$ and I also know the definition of not onto. I don't understand the whole concept of one-dimensional space and would this statement be always true?

asked 2020-11-01

The given matrix is the augmented matrix for a system of linear equations. Give the vector form for the general solution.

$\left[\begin{array}{cccccc}1& -1& 0& -2& 0& 0\\ 0& 0& 1& 2& 0& 0\\ 0& 0& 0& 0& 1& 0\end{array}\right]$

asked 2022-07-25

If A is an n x n matrix , where are the entries on the main diagonal of A-A^T? Justify yoyr answer.

asked 2022-06-26

The problem is this:

The impulse response of a system is the output from this system when excited by an input signal $\delta (k)$ that is zero everywhere, except at $k=0$, where it is equal to 1. Using this definition and the general form of the solution of a difference equation, write the output of a linear system described by:

$y(k)\u20133y(k\u20131)\u20134y(k\u20132)=\delta (k)+2\delta (k\u20131)$

The initial conditions are: $y(\u20132)=y(\u20131)=0$.

My question is: How can the particular solution be found using the method of undetermined coefficients if the non-homogeneous equation is also a difference equation?

The impulse response of a system is the output from this system when excited by an input signal $\delta (k)$ that is zero everywhere, except at $k=0$, where it is equal to 1. Using this definition and the general form of the solution of a difference equation, write the output of a linear system described by:

$y(k)\u20133y(k\u20131)\u20134y(k\u20132)=\delta (k)+2\delta (k\u20131)$

The initial conditions are: $y(\u20132)=y(\u20131)=0$.

My question is: How can the particular solution be found using the method of undetermined coefficients if the non-homogeneous equation is also a difference equation?