5. Answer the following questions. (a) Using elementary row operations, we go from Ax = b to Rx = d, where R is the RREF of A. The complete solution is x = |0+r +s Here, r and s are free parameters. What is the 3 x 3 matrix R in the reduced row echelon form and what is d? (b) In part (a), if the process of Gauss-Jordan elimination to get from A to R subtracted 3 times row 1 from row 2 and then 5 times row 1 from row 3, what are the original matrix A and vector b?

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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5. Answer the following questions.
(a) Using elementary row operations, we go from Ax = b to Rx = d,
where R is the RREF of A. The complete solution is
X =
+r|1+s
Here, r and s are free parameters. What is the 3 x 3 matrix R in the
reduced row echelon form and what is d?
(b) In part (a), if the process of Gauss-Jordan elimination to get from A
to R subtracted 3 times row 1 from row 2 and then 5 times row 1
from row 3, what are the original matrix A and vector b?
(c) If A and B are two general n x n matrices, is it true that (A+ B)? =
A? + 2AB + B? Is it true that (A – B)(A + B) = A² – B²? If
either of these statements is or both of them are untrue, what is/are
the correct statements? You may assume that both left and right
distributive laws hold.
Transcribed Image Text:5. Answer the following questions. (a) Using elementary row operations, we go from Ax = b to Rx = d, where R is the RREF of A. The complete solution is X = +r|1+s Here, r and s are free parameters. What is the 3 x 3 matrix R in the reduced row echelon form and what is d? (b) In part (a), if the process of Gauss-Jordan elimination to get from A to R subtracted 3 times row 1 from row 2 and then 5 times row 1 from row 3, what are the original matrix A and vector b? (c) If A and B are two general n x n matrices, is it true that (A+ B)? = A? + 2AB + B? Is it true that (A – B)(A + B) = A² – B²? If either of these statements is or both of them are untrue, what is/are the correct statements? You may assume that both left and right distributive laws hold.
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