MTH501 Quiz 3 by Junaid

Q1. A partitioned square matrix ‘A’ is said to the matrix if the matrices on the main diagonal square and all matrices above the main diagonal are zero.

Block lower triangular

Q2. if there is a vector v= (2,1,0) then ||v|| is ……..

Q3. Each pair of eigenvalue and its corresponding eigenvectors provide a solution of equation.

Q4. which of the following is true for the matrix

Where M11 .M22 and M33 are square sub – matrices, and O is Zero sub matrix?

It is block upper triangular matrix

Q5. suppose that real solution y1 and y2 of x1 = Ax from a basis for the two- dimensional real vector space if y1 and y2 are ……..

Linearly independent

Q6. Let W be a subspace of R and (u1, u2,…….up) is any orthogonal basis of W, then y = c1u1+ c2u2……… cnun where

Cj = y uj uj uj

Q7. Elementary row operation on a matrix do not affect the ….. relation among the column of the matrix

Linear dependence

Q8. Two vector are ……….. if at least one of the vector is a multiple of the other

Linearly dependent

Q9. Electric circuit rotation is caused by sine and cosine function if there eigenvalues are complex and hence the origin is called….

Spiral point

Q10. Multiplication of a partitioned matrix by a scalar is also computed…..

Column by column

Q11. The invariable Matrix .Theorem applies only to………………

Square

Q12. Let A be a real 2 by 2 matrix with complex eign values  = a – b + I,(b  ) and associated eigenvectors v in C2 then A PCP -1 where p= ------

P = [Revlmv]

Q13. Let Ax = 0 be a homogeneous linear system of ‘n’ unkown , then the cowfficient matrix ‘A’ is invertable if and only if this system has ------------- solution

Trivial

Q14. the two vector are said to b equivalent if

Same length and same direction

Q15. if one of the eigenvalues of [A]nxn is zero .it implies

The determined of [A] is zero

Q16. let be a five – dimensional vector space. And let ba subset of consisting of five vectors.

Mast be linearly dependent , but may or may not span V

Q17. Supposex,y ,z are some vectors in an inner produect space (v,<,>) such that <X,Y>=<X,Z> for all x  V then Y=Z

TRUE

Q18. let U,V and W be vectros in Rn ,then

(U+ v), W=U.W+V.W

Q19. if u and v non zero vector in either R2orR3 then by the law of cosines || u – vii2……..

||u – v||2 = ||u||2 + ||v||2 - 2 ||u||||v||cos

Q20. If u +v – w, then

V = w

Q21. Two vectors u and v in Rn are orthogonal if…………….

u.v = o

Q22. A vector whose length 1 is called ……………..

Q23. A …………. Matrix whit orthogonal columns is an orthogonal matrix.

Square

Q24. if a square matrix has orthogonal columns then it also has …… rows.

Orthogonal

Q25. The norm of v is the non-negative scalar ||v|| defined by

||v|| = V 21 + v22 +………….v2n

Q26. the matrix A ^ T x A is invertable if and only if the columns of A are linearly independent

True

Q27. let V be a one Eigen vector then conjugate eigen vector is repented by.

V----

Q28. Any finite dimensional inner product space an orthonormal basis.

True

Q29. the ……….. vector is orthogonal to every vector in Rn.

Zero

Q30. Each pair of eigenvalue and this its corresponding eigenvector provides a solution of the equation X1 = Ax which is called …………….. of the differential equation.

Q31. if we divide a non – zero vector by its length we get a

Q32. A matrix A – (n\time n) has both positive and negative eigenvalues so in this case origin behave as a

Saddle point