Definition of Kernel and Range of a Linear Transformation and when is a Linear Transformation one to one and onto. Please note, In example 1(a), the point is (0,-3,-3). Sorry for the typing error.
We form an augmented matrix [A:B] by writing all the coefficients of LHS and RHS and then use Gauss elimination method and reduce the matrix to REF form . In the question here we reduced to REF form the last row has all zeros which means system is solvable . When the rank of A = rank of [A:B] we say system is solvable
Thank u very much mam. Very beautifully explained the concept of range and null space
Thank you very much
Hi, question(a) seems wrong, the result is not equal to (0,0,0) and thus (0,3,-3) is not within the kernel.
It is a typing mistake . The point is (0, -3 , -3). Sorry for that.
4:22 how it solvable madam please show it
We form an augmented matrix [A:B] by writing all the coefficients of LHS and RHS and then use Gauss elimination method and reduce the matrix to REF form . In the question here we reduced to REF form the last row has all zeros which means system is solvable . When the rank of A = rank of [A:B] we say system is solvable
The 1st question is incorrect....
It's typing error. The point is. ( 0, -3,,-3). Sorry guys
Sorry it is a typing error. The point is (0, -3, -3).