For aib E 2, let d=ged (2a tb, 3a+2b) la) Prove d is a common dliusor of a & b (6) Prove, d is the greatest comman divicar of an

Q: 5) Expand using special product rules c) (12 – 4x)? d) (3y – 6)2

A: c. Given: Apply special product rule in the above expression.

Q: Verify that (AB)T = BTAT.

A:

Q: Compute AB, where A AT B = = 24 09 4 -3 -1 and B = 76 (1 %). 6 4

A:

Q: (a) [0, 1] (c) {2,7} (e) {÷ :n e N} (g) [0, 1] U [2, 3] (b) (0, 1) (d) {T,e} (f) {0}

A: To find supremum of given sets .

Q: Let u = Compute the following: ū• v = (1, −5, −1) and v = (-5,2,0). v.u ||ū|| ² - 3 (u.v) (-3ū) v =…

A:

Q: TRUE or FALSE: A\B = A when A and B are disjoint

A: Given statement ,A|B=A then A and B are disjoint

Q: U= 2i-35 j V = 59 +3

A: Given: u=2i−3jv=5i+3j

Q: verify that (AB)T = BTAT

A: Given matrices: Now,

Q: Prove that dv du 2 – u? + v² 18

A:

Q: ASTR n = 2x+y 121 x,y € Prove that A is not open and not closed. Q

A:

Q: Let p x²-2x+1, p² = 3 +3x+1 and p³ = 5x + 10. Let q = x³-3x + 4. Is q' in the span of p1, p2 and p³?

A:

Q: Evaluate the commutators [Lz, r²] and [Lz, p²] (where, of course, r² x² + y² +z? and p? = p? + p; +…

A: Given To evaluate the commutators Lz,r2 and Lz,p2 where r2=x2+y2+z2 and p2=px2+py2+pz2.

Q: Suppose FW = Ax+B, with F6)-r and F() - 8, pind F) interms of A,B,r,s

A:

Q: if n(A U B) = 97 and n(A) = n(B) = 69, find n( A ∩ B)

A: We are asked to find n(A∩B)