1.
If A is a 4x3 matrix, is Ax=b consistent for every b in R^4? explain
Solution
If A is a 4x3 matrix, is Ax=b consistent for every b in R^4? explain
Simple answer is NO.
When we will row reduce a matrix with 4 rows and 3 columns, then some values of b in R^4 can
lead to SUM OF ZERO COEFFICIENTS EQUAL TO NON ZERO REAL NUMBER because
maximum number of pivots in 4x3 matrix will be 3 (which is the number of columns) but rows
are 4. So, when we will row reduce a matrix, then 4th row can lead to sum of zero coefficients
equal to non-zero real number which means INCONSISTENCY in the system.
Therefore, such system will not be consistent for every value of B.