Row equivalence. What is it exactly? When matrices are row equivalent... why is this important? If a matrix like: [10−11] is row equivalent to the identity matrix (add 3 times the first row to the second), what does that mean exactly? Why is this a concept that we have to know as students of linear algebra? These matrices arent

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Row equivalence. What is it exactly?  When matrices are row equivalent... why is this important? If a matrix like:  [10−11]  is row equivalent to the identity matrix (add 3 times the first row  to the second), what does that mean exactly? Why is this a concept that  we have to know as students of linear algebra? These matrices arent

einfachmoipf · Accepted Answer

[10|0−31|0]R2⇒R2+3R1&amp;nbsp;(1)[10|001|0]&amp;nbsp;(2)The information is conveyed via the related system of homogeneous equations above.x = 0 x = 0 −3x + y = 0 y=0⇒&amp;nbsp;A matrix&#039;s row space is unaffected by simple row operations. In particular, the row space is the same for any two row equivalent matrices.⇒&amp;nbsp;If and only if they are equivalent, two matrices of reduced row echelon form will share the same row space.

Donald Cheek · Accepted Answer

The solutions to the two matrix equations Ax=b and Bx=b are the same as long as A and B are row equivalent, which is why I believe the idea of row equivalence to be crucial.&amp;nbsp;It is frequently desirable to convert a metric problem Ax=b into an equation Bx=b that is simpler to solve since row operations do not alter the solution set.

Row equivalence. What is it exactly? When matrices are row equival

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