Mth501 quiz no3 spring solution 2023

Mth501 quiz no3 spring solution 2023
The process of creating the unit vector u from v sometime called--------

A system of linear equations is said to be homogeneous if it can be written in the form _______

An n x n matrix A is invertible if and only if ___________ is not an eigen value of A.

A null space is a vector space.

If one of the eigenvalues of [A]n×n[�]�×� is zero, it implies -------

Elementary row operations on a matrix do not affect the -------- relations among the columns of the matrix.

If u + v =u + w, then:

If the augmented matrices of two linear systems are row equivalent, then the two systems have the ______ solution set.

Let u, v and w be vectors in Rn��, then

Any set of three non-coplanar vectors {a,b,c} in ordinary space spans the -------- space

The product of upper triangular matrices is

If u� and v� are non zero vectors in either R2�2 or R3�3 then by the law of cosines ||u−vII2||�−���2=---------

Which one of the following is a null matrix?

Let A� be a real 2 by 2 matrix with complex eigen values λ=a−b+i,(b≠0)�=�−�+�,(�≠0) and associated eigenvectors v� in C2�2, then A=PCP−1�=���−1, where P=−−−−−

For u and v vectors in Rn��, thw distance between u and v written as dist(u,v)����(�,�) is the length of the vector-----

A system of linear equations is said to be homogeneous if it can be written in the form _________

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