(a - b)(a − c)(a − d)(b − c)(b − d)(c - d) -

Q: | V1 – 47² dx.

A: We know that sin2(u)+cos2(u)=1   ⇒ 1-sin2(u)=cos2(u) cos2(u)=121+cos(2u) sin2 sin-1y = 2y1-y2

Q: (c) Show that (AB)² + (A x B)² = (AB)².

A: Given ( A.B )2 + ( A×B )2 = ( AB )2

Q: (1) (0) 2メー+3X+5 =D (b) -4 4 and jo 2 j13 (c) 442-5t+7 -D

A:

Q: If a 2 × 2 matrix A is non-invertible, then the image of the unit square under the linear…

A: False Reason : Here the image of unit square image

Q: Find, if possible, (a) A + B, (b) A − B, (c) 2A, (d) 2A − B,and (e) B + 1/2 A.

A: a). b).

Q: Show that 2 (-r × B)² = (r² B² – (r. B)²) And, further that r² B² (r. B)² = B² (x² + y²) - If B = B₂

A:

Q: b) (x-1)² 4 (y + 2)² 9 = −1 5 -5 5

A: This is the standard form of a hyperbola that opens up and down. Let's identify its properties…

Q: Cx-3) Gょ2)tG3)

A:

Q: Find det(B)

A: Given that: det-1A-1=-5=detA3B-1T-1A-1=-5=A3B-1T As we know, detkM=kndetkM and detM=1detM-1. (Here,…

Q: B=i-3)-k , A= 31-j+k ti-B+č=0 (C) asiall asaa

A:

Q: Find (a) u − v, (b) 2(u + 3v), and (c) 2v − u. u = (−7, 0, 0, 0, 9), v = (2, −3, −2, 3, 3)

A: a). b).

Q: (9х2 — 9х — 10) : (3х — 2)

A:

Q: If 2A=3B and 4B=5C  (i) A:C (ii) A:B:C

A:

Q: Provide counterexamples for If (A −B) ∩ (A −C) = ∅, then B ∩ C = ∅.

A: The solution is given as

Q: Show that (A + B)2 is not equal to A2 + B2 by showing that this is not true with A = 3 and B = 2.…

A:

Q: (b) y 4 X -2 4 -2 -4 y = 2. 2.

A: Given graph is:   To find the y.

Q: (8) lf (a-b-a) za 2b 29 (b-a-c) 2b = K²(a+b+c) ³ 2C (c-α-b) then K=

A: Given:a-b-c2a2a2bb-a-c2b2c2cc-a-b=ka+b+c3    .............1We need to find the value of k.

Q: Find, if possible, (a) A + B, (b) A − B, (c) 2A, (d) 2A − B,and (e) B + 1/2 A.

A:

Q: Find (a) c23 and (b) c32, where C = 5A + 2B,

A:

Q: If n(A) = 104, n(A U B) = 141, and n(A n B) = 42, find n(B).

A:

Q: Multiply: . (V3 + V7)? b. (V7 + V5) (V7 - V3) c. (Va – V5) (Vā + V6). а.

A: The given expression is 3+72  3+72=32+237+72=3+221+7=10+221

Q: (9) [xV1-2х dx

A: