2 Q) Let A € M₁ C4) such that A² = A ENA show that det (I+A) = 2

Q: 2. Let A = 201-18 and /= 2 1 1 2 01 Find A(A+1).

A: A=[2 1      1 2]I=[1 0      0 1]

Q: Prove that A u (B n C) = (Au B) n (A u C).

A:

Q: Find the multiplicative inverse mod n of x. Your answer should be an integer s in the range 0…

A:

Q: Prove that: (5a + 6b|a, b = Z} = Z

A: To prove that .Concepts used:Consider two sets  and . To prove that , we first need to show and…

Q: 2) Let R' real numbers, define = x,Y1 + 3x2y; + 5x3y3 for x = (x, X2, X3) and y (y,Yz, Y3). Is…

A: Given x=x1,x2,x3, y=y1,y2,y3 in ℝ3. Define x,y=x1y1+3x2y2+5x3y3

Q: If u * v = 2i - 3j + k, what is v * u?

A: As we know a×b = - b×a

Q: Show that is isomorphic to Z2.

A:

Q: If Z- N(0,1), then P(0.33<Z<1.05) is: a) b) 0.129 0.353 c) d) 0.224 0.482 Accesibilidad todo corredo

A: Given : Z ~ N(0, 1)

Q: Let x) 4 and gx)-x-3. Find the foilowing lock

A: To find the following expressions

Q: Show that if AB = I, then det(A) 0 and det(B) # 0.

A: Here given as AB=In find determinant both sides detAB=detIndetAB=1

Q: Hiw.sLetAzi+j-2K,b=-i-k and c=zi+uj-zk,finds t Ax(B+C)- 3 CA-B)xC s-(AXB)ec 2- A (2B-c) 4-2Ax 3B 6-…

A:

Q: j+ky-o Find k Iet yco)=lo0 andyc2)=4 3D0

A: Given that y'+ky=0 y(0)=100 and y(2)=4

Q: Show that S = {x* + 1, xª + x, xª + a², xª + æ*, xª} spans PA.

A:

Q: xʻy Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (x4+6y8) r4.

A:

Q: a) Define AAB = (A − B) U (B − A), where A, B are any two sets. Show that (ΑΔΒ)ΔC = ΑΔ(ΒΔC).

A:

Q: Let z=x+iy  Let w=a+ib

A: To prove the equality of the two given angles

Q: Show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

A: We have to show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…

A:

Q: Show that (AB)T and BTAT are equal.

A: Now,

Q: Cietni let ane let G4)= ti t2+34)j +4K HIC4) = 2,4し + 34j+(-144)1k fnd の) H4)XG(H) b) G4). HG4)

A: Given: Gt=ti+2+3tj+4kHt=2ti+3tj+-1+2tk

Q: 6. show that the set A = {P= (₁4₁2) (R³ | 1²4 + √²2+x2 is an open out.

A:

Q: Determine s, t eZ where gcd(222, 921) = 222s + 921t.

A: I have used division algorithm to solve the problem

Q: Prove that du Inlul + C where n= -1 u

A:

Q: how that ℝ3 = span( 1 1 2 1 2 1 0 3 -1

A: We want to show that  any vector can be written as linear combination of the three  given vectors…

Q: A (T+ 7) = A·I+ A ·G A (c.F) = c · (A · T) Verify these two properties by direct computation in the…

A:

Q: 2 O Expand Pn = 2x +3x +) in Term of P.f,.

A:

Q: Find a number z (except 0) such that Az³ + Bz²+ Cz = D 2 1 3 0 -2 -4 00 ^-[ ] ³-R2 :]-[+]-[1] B= 1 2…

A: Solution

Q: Let x, y € Z. Prove that if 2 | (x² - y2) then 4 | (x² - y²)

A: We know that the sum of two odd numbers is an even number.Also, the difference between two odd…