JSFH A := <<1,1+I,2+I>|<-1,-1+I,-2+I>|<I,1-I,lambda>>;

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b := Vector([1,I,1+I]);

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpP1RYJyo=

with(LinearAlgebra): ReducedRowEchelonForm(<A|b>);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKVdNPiUp

MatrixInverse(A);

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B := subs(lambda=1,A);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKTsrVyYq

ReducedRowEchelonForm(<B|b>);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKSkpUW0kKQ==

LinearSolve(A,b);

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LinearSolve(B,b);

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JSFH Page 87, #4 A := <<1,3>|<2,lambda>>;

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MatrixInverse(A);

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When \316\273=6, there is no inverse. Or A is singular. Then Ax=0 has infinintely many solutions. Otherwise (\316\273\342\211\2406), Ax=0 has a unique solution x=0. For part (b). b1 := Vector([1,3]);

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JSFH When \316\273\342\211\2406, the matrix A is nonsingular. Therefore, Ax=b1 always has a unique solution. B := subs(lambda=6,A);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKVcsayQp

ReducedRowEchelonForm(<B|b1>);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKTcmUVUp

Ax = b1 is always consistent for whatever \316\273. (c) b2 := Vector([1,1]);

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ReducedRowEchelonForm(<B|b2>);

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JSFH The system Ax=b2 is inconsistent for \316\273=6 How to type a matrix or vector: x_1 : LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJ0Y+ x_3^2 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobXN1YnN1cEdGJDYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0YyRjUtRiM2JS1GOzYkUSIyRidGPkYyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUvc3Vic2NyaXB0c2hpZnRHRkcvSSttc2VtYW50aWNzR0YkUSxbbm9uZSxub25lXUYnRj4= 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 TTdSMApJNVJUQUJMRV9TQVZFLzk1NTc2NjUyWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQiIiJeJEYnRideJCIiI0YnISIiXiRGK0YnXiQhIiNGJ14jRideJEYnRislJ2xhbWJkYUdGJg==TTdSMApJNVJUQUJMRV9TQVZFLzk2NDU0MTIwWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkIiIiXiNGJ14kRidGJ0YmTTdSMApJNVJUQUJMRV9TQVZFLzg0MTkzNDQ0WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjLSIkIiUiIiIiIiFGKEYoRidGKEYoRihGJ14kRicjRiciIiNeI0YqRihGJg==TTdSMApJNVJUQUJMRV9TQVZFLzk2NDQwNzcyWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQqKF4jIyEiIiIiIyIiIiwoJSdsYW1iZGFHRioqJl4jRixGLEYuRixGLF4kRiwhIiRGLEYsLCZGLkYsRipGLEYqKiheIyNGLEYrRiwsKEYuRixGL0YsXiRGMkYsRixGLEYzRiosJCokRjNGKkYqKihGNUYsLCZGLkYqXiRGLEYrRixGLEYzRioqKEY1RiwsJkYuRipeJEYqRitGLEYsRjNGKkY5RjoqJl4kRixGLEYsRjNGKkY6RiY=TTdSMApJNVJUQUJMRV9TQVZFLzk1NDQwMDE2WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQiIiJeJEYnRideJCIiI0YnISIiXiRGK0YnXiQhIiNGJ14jRideJEYnRitGJ0YmTTdSMApJNVJUQUJMRV9TQVZFLzgzNjYzODg4WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjLSIkIiUiIiIiIiFGKEYoRidGKCEiIl4kRilGKUYoXiRGJyNGJyIiI14jRixGKEYmTTdSMApJNVJUQUJMRV9TQVZFLzg0MzM4MDUyWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkXiQiIiIjRigiIiNeI0YpIiIhRiY=TTdSMApJNVJUQUJMRV9TQVZFLzgzNTk2MzY0WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkLCheJCMiIiQiIiUjIiIiRitGLSYlJF90MEc2IyIiIyNGLUYxKiZeIyMhIiJGMUYtRi5GLUYtRi4sKF4kI0Y2RitGOUYtRjNGLUYuRjJGJg==TTdSMApJNVJUQUJMRV9TQVZFLzk1MjkxNzI0WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJSIjIiMiIiIiIiQiIiMlJ2xhbWJkYUdGJg==TTdSMApJNVJUQUJMRV9TQVZFLzgzODI3NDE2WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJSIjIiMqJiUnbGFtYmRhRyIiIiwmRihGKSEiJ0YpISIiLCQqJEYqRiwhIiQsJEYuISIjRi5GJg==TTdSMApJNVJUQUJMRV9TQVZFLzk2NTA4NTYwWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjIiIiIiIkRiY=TTdSMApJNVJUQUJMRV9TQVZFLzgzNjQwMTQ0WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJSIjIiMiIiIiIiQiIiMiIidGJg==TTdSMApJNVJUQUJMRV9TQVZFLzg0MjM4NTEyWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJyIjIiQiIiIiIiEiIiNGKEYnRihGJg==TTdSMApJNVJUQUJMRV9TQVZFLzgzODkwOTQ4WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjIiIiRidGJg==TTdSMApJNVJUQUJMRV9TQVZFLzg0MjExNDQwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJyIjIiQiIiIiIiEiIiNGKEYoRidGJg==TTdSMApJNVJUQUJMRV9TQVZFLzg0MTQ1MzI0WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkJiUibUc2JCIiIkYqJkYoNiQiIiNGKiZGKDYkIiIkRipGJg==