Q1) Reduce the following matrices to row echelon form and row reduced echelon forms:
Q2) (i) Determine the currents for the electrical network shown in the following figure, using Gauss elimination:
(ii) Find the volume of traffic along the arrows, using Gauss elimination:
Q3) What situation arises in accordance with the Fundamental Theorem of linear algebra for the systems given below:
Q4) A) Find a family of the matrices that is similar to the matrix
B) Find eigenvalues and eigenvectors of the following matrix: Determine (i) Eigenspace of each eigenvalue and basis of this eigenspace (ii) Eigenbasis of the matrix
C) Is the matrix in part(b) is defective?
Q 5) A) Find the eigenbasis of the matrix and diagonalize it (if possible):
B) For the matrix in part (i), find A2 and A 1 theorem. using Cayley-Hamilton THEORM.
Q6) A) Sketch the vector and scalar fields. Describe the nature of vector fields. [5] Find also Curl and divergence in parts (i)-(iii). In parts (iv) and (v), find a unit normal to the given surface at a point of your choice.
check the attached file for all the quastions and requirements
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