Mathematics

Q..

Objective Part

Write short ansivers of the following in 2-3 lines each.

Define zero vector space.

Compute tv and ku for u= (-1,2), v= (3,4), and k-3.

Piline Linearly independent

(Compulsory)

(2"16)

IX.

XII.

xili.

XIV.

XV.

xvi.

Q.2.

Q.3.

Q.4.

Define row space.

Detine characteristic equation.

Date seat ear in, mity and dimension of yow.gaim.pli.com

Find eigen values of the matrix A -

Define unit vector.

Define orthogonal vectors:

If u and v are orthogonal vectors in a real inner product space, then

Find the cosine of the ungle between the vectors w.rt Euclidew inner product

u = (1-3), v = (24)

Determine whether the vectors ure orthogonal wirt the Euclidean inner product

и = (-1,3,2), 0 - (4.2, -

1)

Subie ive Part

(3*16)

(a) State and prove Cauchy Schwarz Inequality.

(b) State and prove Triangle Inequality.

(a) Show that the vectors

P, = (1,2.1), v2 = (2,9,0), v, = (3,3.4)

form a basis for R3

(b) Write the procedure for diegonalizing an nsn matrix.

Find the inverse of

dastahi.pk

12 3

00.00

81

(b) Use Cramer's rule to solve

xy + 2xg = 6

-3x1 + 4x2 + 6x3 = 30

-*, - 2* visit website: ustani.pk ustadni.com