Question: Given a system of linear equations a x 1 + a x 2 + a x 3 = 2 x 1 + a x 2 + a x 3 = 0 2 x 1 + 3 x 2 + a x 3 = 1For what 2 values of a will the system's augmented matrix have less than 3 pivots?I'm not looking for an answer to the question, but I'm currently using trial and error to try and form a row 0000, and was wondering if there's some conceptual understating I'm missing that would point to a more logical strategy for finding a?

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Question: Given a system of linear equations  a      x    1    +  a      x    2    +  a      x    3    =  2        x    1    +  a      x    2    +  a      x    3    =  0    2      x    1    +  3      x    2    +  a      x    3    =  1For what 2 values of   a will the system&#039;s augmented matrix have less than 3 pivots?I&#039;m not looking for an answer to the question, but I&#039;m currently using trial and error to try and form a row 0000, and was wondering if there&#039;s some conceptual understating I&#039;m missing that would point to a more logical strategy for finding   a?

gaiageoucm5p · Accepted Answer

Use algebra, and perhaps expansion by minors, to find the determinant of the matrix of coefficients      [                            a                          a                          a                                      1                          a                          a                                      2                          3                          a                      ]  I believe you get a cubic polynomial. Set the resulting expression equal to zero and solve for   a. Check each of those solutions to see if the resulting original equations have zero solutions or infinitely many solutions.

Question: Given a system of linear equations a x 1 </msub> + a

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