b1 b2 b3 1-4-3 Let A -4 4 0 and b = Show that the equation Ax = b does not have
ID: 3169683 • Letter: B
Question
b1 b2 b3 1-4-3 Let A -4 4 0 and b = Show that the equation Ax = b does not have a solution for all possible b, and describe the set of all b for which Ax:b do s have a solution. A. Row reduce the matrix A to demonstrate that A does not have a pivot position in every row. 0 B. Find a vector b for which the solution to Ax= b is the zero vector O c Row reduce the augmented matrix A b 1 to demonstrate thatA b 0 D. Find a vector x for which Ax = b is the zero vector. has a pivot position n every row. E. Row reduce the matrix A to demonstrate that A has a pivot position in every rov. Describe the set of all b for which Ax= b does have a solution. 0- Type an expression using by,2,and b3 as the variables and 1 as the coefficient of b3)Explanation / Answer
To determine whether the equation Ax = b has a solution for every b or not, we will reduce A to its RREF as under:
Add 4 times the 1st row to the 2nd row
Add -3 times the 1st row to the 3rd row
Multiply the 2nd row by -1/12
Add -12 times the 2nd row to the 3rd row
Add 4 times the 2nd row to the 1st row
Then the RREF of A is
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The last row of the RREF of A is zero. It implies that the columns of A do not span R3. Hence if the vector b has a non-zero entry in the last row, i.e. if b30, then the equation Ax = b will not have a solution The option A is the correct answer.
If b3=0 i.e. if b = { (b1,b2,0)T| b1,b2 R}, then the equation Ax = b will have a solution
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