Lights Out 3 2 0 8

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Lights Out 3 2 0 8

Career: 26-32, 225 SV (42nd), 3.54 ERA, 799 SO, P, 2xAllStar, Astros/Phillies/. 2002-2012, t:R, born in CA 1976, Lights Out. Lights-Out – Nomen est omen – The name says it all. Lights-Out is a power and runtime management solution and works according to the motto. The last one turns out the light! Lights-Out can be used in a Small Business or Home Environment.Lights-Out has been proven in use for years and is as popular with family administrators as it is with company administrators. Lights-Out 2.0 released New 2.0, News 2 After more than 1 year of development, we are proud to announce the immediate availability of Lights-Out 2.0 on November 11, 2016!

Windows Phone 8, Windows Phone 8.1, Windows 10 or later UHD Xbox One S or Xbox One X with a connection to a 4K television over HDMI 2.0a with support for HDCP 2.2. An HDR-capable television is required to view in High Dynamic Range. 5.0 out of 5 stars Lights out 3. Reviewed in the United States on January 3, 2014. Verified Purchase. I got this cd for my husband for Christmas and he loved it! He had been talking about for quite a long time, so I wanted to surprise him. I love to see him smile!
A system of linear equationsSolving the (3 times 3) version of Lights Out amounts tosolving the system (Ax=b) over (GF(2)) where(A = begin{bmatrix}1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0  1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0  0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0  0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0  0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1  0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0  0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1  0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 end{bmatrix})and (b = begin{bmatrix}b_1  b_2  b_3  b_4  b_5  b_6  b_7  b_8  b_9 end{bmatrix}).
Recall that column (i) of (A) represents the action of pressing square (i); the entries in the column equal to 1 correspondto the squares that are toggled when square (i) is pressed.
Lights Out 3 2 0 87The tuple (b) represents the configuration of lights.Hence, (b_i = 1) if and only if the light at square (i) is on.
The variable (x_i) corresponds to square (i) and is set to 0 or 1.It is set to 1 if and only if the corresponding square needs to be pressedin a solution of the game.
We now solve the system using row reduction. https://herejfile362.weebly.com/pompeii-casino-game.html. The following table shows the entire process.Separating lines have been added to the matricesto aid reading. https://bestufil613.weebly.com/zorro-slot-machine.html.

Windows Phone 8, Windows Phone 8.1, Windows 10 or later UHD Xbox One S or Xbox One X with a connection to a 4K television over HDMI 2.0a with support for HDCP 2.2. An HDR-capable television is required to view in High Dynamic Range. 5.0 out of 5 stars Lights out 3. Reviewed in the United States on January 3, 2014. Verified Purchase. I got this cd for my husband for Christmas and he loved it! He had been talking about for quite a long time, so I wanted to surprise him. I love to see him smile!
A system of linear equationsSolving the (3 times 3) version of Lights Out amounts tosolving the system (Ax=b) over (GF(2)) where(A = begin{bmatrix}1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0  1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0  0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0  0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0  0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1  0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0  0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1  0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 end{bmatrix})and (b = begin{bmatrix}b_1  b_2  b_3  b_4  b_5  b_6  b_7  b_8  b_9 end{bmatrix}).
Recall that column (i) of (A) represents the action of pressing square (i); the entries in the column equal to 1 correspondto the squares that are toggled when square (i) is pressed.
Lights Out 3 2 0 87The tuple (b) represents the configuration of lights.Hence, (b_i = 1) if and only if the light at square (i) is on.
The variable (x_i) corresponds to square (i) and is set to 0 or 1.It is set to 1 if and only if the corresponding square needs to be pressedin a solution of the game.
We now solve the system using row reduction. https://herejfile362.weebly.com/pompeii-casino-game.html. The following table shows the entire process.Separating lines have been added to the matricesto aid reading. https://bestufil613.weebly.com/zorro-slot-machine.html.
Lights Out 3 2 0 805begin{align*}~ & left[scriptsizebegin{array}{ccc|ccc|ccc|c}1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & b_1 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & b_2 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & b_3  hline1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & b_4 0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & b_5 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & b_6  hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & b_9end{array}right] xrightarrow{R_2 leftarrow R_2 + R_1}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & b_1 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & b_1+b_2 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & b_3  hline1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & b_4 0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & b_5 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & b_6  hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & b_9end{array}right] xrightarrow{R_1 leftarrow R_1 + R_4}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & b_1+b_4 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & b_1+b_2 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & b_3  hline1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & b_4 0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & b_5 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & b_6  hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & b_9end{array}right] xrightarrow{scriptsizebegin{array}{c}R_3 leftarrow R_3 + R_1  R_5 leftarrow R_5 + R_1end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & b_1+b_4 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & b_1+b_2 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & b_1+b_3+b_4  hline1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & b_4 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & b_1+b_4+b_5 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & b_6  hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & b_9end{array}right] xrightarrow{scriptsizebegin{array}{c}R_2 leftarrow R_2 + R_3 R_6 leftarrow R_6 + R_3end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & b_1+b_4 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & b_2+b_3+b_4 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & b_1+b_3+b_4  hline1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & b_4 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & b_1+b_4+b_5 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_1+b_3+b_4+b_6  hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & b_9end{array}right] xrightarrow{scriptsizebegin{array}{c}R_2 leftarrow R_2 + R_7  R_4 leftarrow R_4 + R_7 R_5 leftarrow R_5 + R_7end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & b_1+b_4 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & b_2+b_3+b_4+b_7 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & b_1+b_3+b_4  hline1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & b_4+b_7 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & b_1+b_4+b_5+b_7 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_1+b_3+b_4+b_6  hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & b_9end{array}right] xrightarrow{scriptsizebegin{array}{c}R_1 leftarrow R_1 + R_8  R_3 leftarrow R_3 + R_8 R_4 leftarrow R_4 + R_8end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & b_1+b_4+b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & b_2+b_3+b_4+b_7 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & b_1+b_3+b_4+b_8  hline1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_4+b_7+b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & b_1+b_4+b_5+b_7 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_1+b_3+b_4+b_6  hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & b_9end{array}right] xrightarrow{scriptsizebegin{array}{c} R_2 leftarrow R_2 + R_5  R_3 leftarrow R_3 + R_5 R_9 leftarrow R_9 + R_5end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & b_1+b_4+b_8 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & b_1+b_2+b_3+b_5 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & b_3+b_5+b_7+b_8  hline1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_4+b_7+b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & b_1+b_4+b_5+b_7 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_1+b_3+b_4+b_6  hline0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & b_7 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & b_8 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & b_1+b_4+b_5+b_7+b_9end{array}right] xrightarrow{scriptsizebegin{array}{c} R_4 leftarrow R_4 + R_6 R_7 leftarrow R_7 + R_6R_8 leftarrow R_8 + R_6end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & b_1+b_4+b_8 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & b_1+b_2+b_3+b_5 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & b_3+b_5+b_7+b_8  hline1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & b_1+b_3+b_6++b_7+b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & b_1+b_4+b_5+b_7 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_1+b_3+b_4+b_6  hline0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & b_1+b_3+b_4+b_6+b_7 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & b_1+b_3+b_4+b_6+b_8 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & b_1+b_4+b_5+b_7+b_9end{array}right] xrightarrow{scriptsizebegin{array}{c}R_1 leftarrow R_1 + R_9  R_3 leftarrow R_3 + R_9 R_7 leftarrow R_7 + R_9end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & b_5+b_7+b_8+b_9 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & b_1+b_2+b_3+b_5 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & b_1+b_3+b_4+b_8+b_9  hline1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & b_1+b_3+b_6++b_7+b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & b_1+b_4+b_5+b_7 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_1+b_3+b_4+b_6  hline0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & b_3+b_5+b_6+b_9 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & b_1+b_3+b_4+b_6+b_8 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & b_1+b_4+b_5+b_7+b_9end{array}right] xrightarrow{scriptsizebegin{array}{c}R_8 leftarrow R_8 + R_2  R_9 leftarrow R_9 + R_2end{array}}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & b_5+b_7+b_8+b_9 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & b_1+b_2+b_3+b_5 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & b_1+b_3+b_4+b_8+b_9  hline1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & b_1+b_3+b_6++b_7+b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & b_1+b_4+b_5+b_7 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & b_1+b_3+b_4+b_6  hline0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & b_3+b_5+b_6+b_9 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & b_2+b_4+b_5+b_6+b_8 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & b_2+b_3+b_4+b_7+b_9end{array}right] xrightarrow{R_6 leftarrow R_6 + R_9}~ &left[scriptsizebegin{array}{ccc|ccc|ccc|c}0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & b_5+b_7+b_8+b_9 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & b_1+b_2+b_3+b_5 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & b_1+b_3+b_4+b_8+b_9  hline1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & b_1+b_3+b_6+b_7+b_8 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & b_1+b_4+b_5+b_7 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & b_1+b_2+b_6+b_7+b_9  hline0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & b_3+b_5+b_6+b_9 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & b_2+b_4+b_5+b_6+b_8 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & b_2+b_3+b_4+b_7+b_9end{array}right]end{align*}Slot machine game apps. From the final augmented matrix, we see that(begin{bmatrix}x_1x_2x_3x_4x_5x_6x_7x_8x_9end{bmatrix}=begin{bmatrix}b_1+b_3+b_6+b_7+b_8 b_5+b_7+b_8+b_9 b_1+b_3+b_4+b_8+b_9 b_3+b_5+b_6+b_9 b_2+b_4+b_5+b_6+b_8 b_1+b_4+b_5+b_7 b_1+b_2+b_6+b_7+b_9 b_1+b_2+b_3+b_5 b_2+b_3+b_4+b_7+b_9 end{bmatrix}.)
Hence, if the top-left square is the only one with the light on, thenthe solution is to press squares 1, 3, 6, 7, and 8. (Why?)
ExercisesLights Out 3 2 0 895Solve the (4 times 4) version of Lights Outcompletely. Is there a solution for every possible configuration of lights? Explain your answer.