In Exercises 25–26, determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions.
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Chapter 1 Solutions
Elementary Linear Algebra: Applications Version
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- In Exercises 7–10, the augmented matrix of a linear system hasbeen reduced by row operations to the form shown. In each case,continue the appropriate row operations and describe the solutionset of the original systemarrow_forwardIn Exercises 13–17, determine conditions on the bi ’s, if any, in order to guarantee that the linear system is consistent. 13. x1 +3x2 =b1 −2x1 + x2 =b2 15. x1 −2x2 +5x3 =b1 4x1 −5x2 +8x3 =b2 −3x1 +3x2 −3x3 =b3 14. 6x1 −4x2 =b1 3x1 −2x2 =b2 16. x1 −2x2 − x3 =b1 −4x1 +5x2 +2x3 =b2 −4x1 +7x2 +4x3 =b3 17. x1 − x2 +3x3 +2x4 =b1 −2x1 + x2 + 5x3 + x4 = b2 −3x1 +2x2 +2x3 − x4 =b3 4x1 −3x2 + x3 +3x4 =b4arrow_forwardIn Exercises 7-10, find a linear equation that has the same solution set as the given equation (possibly with some restrictions on the variables). 2x+y=73yarrow_forward
- Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the system have exactly one solution?arrow_forwardIs it possible for a system of equations composed of a linear function and a quadratic func- tion to have 2 solutions? A It is possible for a system of equations composed of a linear function and a quadratic function to have 2 solutions. B It is not possible for a system of equations composed of a linear function and a qua- dratic function to have 2 solutions.arrow_forwardExercise 3.3.2. a) Verify that the system =31has the two solutions e4t and 1e-2. b) Write down the general solution. c) Write down the general solution in the form x?, x2 ? (i.e. write down a formula for each element of the solution)arrow_forward
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