Q–3:| a) Find all m > 1 such that 27 = 9 (mod m). [1 о 1] b) If A = |0 1 1 is a zero-one matrix, find A A A2]. li o ol b) Find the inverse of the encrypting function f(x) = (5 – x) mod 26,0 < x < 25, and use it to decrypt the message "ZRQUBFNB".

Q: Draw vector 1/2CD - 2FE

A:

Q: Compute (-1AT + 2B) C, where A = (-14T +2B) C = 9 7 4 -3 7 -5 " B = -5 9 -4 6 7 3 and C= 6 3 () -3 7…

A: To find (-1AT+2B)C

Q: Let A be 4x4 and det(A)=3. Then det(24)=. and det (A" A)=.

A: Given A be a 4×4 matrix and detA=3

Q: Show that MnXn and Rn^2 are isomorphic.

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Q: 2.x1 + x2 - 8x3 = 0, %3D 3x1 – 2x2 - 5x3 = 0, 41. 5x1 – 6x2 - 3x3 = 0, 3x1 – 5x2 + x3 = 0.

A:

Q: Find the coefficient of z in -5 "Co-"C +"C2 +(-1)" 27

A: Consider the given binomial expansion: C0n-C1n2x-1x+C2n2x-1x2-.......+-1n2x-1xn Here, the objective…

Q: Suppose A = {a1, . . . , am} and B = {b1, . . . , bn}. How many relations are there from A to B?…

A:

Q: Suppose A = [ A²: 13 -30 5 -12 Find an invertible matrix P and a diagonal matrix D so that A =…

A:

Q: a) Find all such that . b) If is a zero-one matrix, find. b) Find the inverse of the encrypting…

A: Clear explanation is given below find the answer below

Q: If A²=0, prove that A cannot be invertible.

A: Given,If A²=0, prove that A cannot be invertible.

Q: et A be m x n and let  be in R^n. If A has a row of zeros, show that Ax has a zero entry

A: We have to solve given problem:

Q: Write down the (1,1) entry of [1 3 A 2 4 7

A:

Q: 9. Assume that the stated inverses exist, prove (A+ B)-1 = A-'(A-1+B-!)-'B-1.

A: Here we prove a equivalent statement.

Q: Suppose I + AB is invertible. Show that I + BA is also invertible by showing that (I + BA)¯ = I –…

A: Assume that I+AB is invertible.  Then, I+ABI+AB-1=I ⋯ 1. Use equation (1) and calculate…

Q: Show that the matrices [1 1 1] A = |1 3 0 and B = |0 o 0 0 1 1 1 1 are similar.

A:

Q: Find the inverse of the following matrix: -7 5 -6 5 -2 3 1 −1 1

A: Given matrix: We have to find the inverse of the given matrix.

Q: Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

A:

Q: 1. Use row operations to find the inverse of '1 1 2 3 6 5 3 3 7

A: Solve for the inverse of the matrix

Q: 5. Compute Jo Jitvx 1 dx -2

A:

Q: Suppose v4 = 20 – 02 + 503. Let w = 601 + 202 – 303 – 204. (a) Write w as a linear combination of…

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Q: If Z=1/√2+i/√2 then the value of conjugate of Z^5= ؟

A: We have z=12+i2 Now, a complex number z=a+ib can be written in polar form as: z=a+ib=rcosθ+i sinθ…

Q: ^= Let A 8 -1 1-2 1 5, let b: ↓ tb=| [3] the set of all linear combinations of the columns of A. and…

A: A=206-1851-21, b=1033 W be the set of all linear combinations of the columns of A. i.e. W=span2-11,…

Q: 6 -1 Let A =| 0 -2 and B . Compute (AB)". Show your work. 4 3

A:

Q: y QI:: Let X₁, X₂ ~ N(0,1) 1) X1-X₂ X₁ + X2 2) (x1+x²)2 X₁-X2 what dist of 2X² 3) x² + x²

A:

Q: Find the integer (a+b) with respect to the module 2,3,5 if a=11 and b=13

A:

Q: 100 If A* = a + bi, compute for a and b.

A: To compute and a and b.

Q: Sole the ff ty Cramer's Rule 4x + + 2 +W 9. 3x + -Z +w - ty -52 + 8w =-3 7x + 4 + z + 2w = 3

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Q: .

A: Given

Q: Find gcd(1000, 34) and lcm(1000, 34) and verify that gcd(1000, 34) · lcm(1000, 34) = 1000 · 34

A: 1000 can be written in the form of prime factors as 1000=2×2×2×5×5×5 34 can be written in the form…

Q: For each 2 x 2 real matrix A find the canonical form B and an invertible matrix P such that P-1AP =…

A:

Q: A=[1 2 3 5, 9 13 26 15, 4 -1 0 3, 6 9 11 7] compute A-1

A: Given matrix is  A = 123591326154-10369117 find A-1

Q: a) If Z1 = -3 + 3i and Z2 = 4i. Show that: i) Arg(Z,Z2) + Arg(Z,) + Arg(Z2) ii) Arg (2) = Arg(Z,) –…

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Q: : 21 = |-1/v2 1/V2-1 1/V2 1/V2]1 o 01-1/v2 1/V2 31[ 1/V2 1/v2] Given the diagonalized matrix A =…

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Q: If A = 3) (a) A + B 2 -6 9 and B = X (b) B-A (c) 2A + 3B -1 J ↓ 1 -10), find A + B, B-A, and 2A +…

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Q: 11. Prove that similar matrices have the same characteristic polynomial.

A:

Q: Verify that (AB)T = BTAT.

A: Now,

Q: Suppose that B = (CEED-·B·CD) -5 and C= 0 are ordered bases of R³. Find the conversion matrix from B…

A: Concept: A vector r is said to be a linear combination of vectors a ,b and c.. etc., if there exist…

Q: write down in se quence steps in finding the the inverse OF matrix using the adjoint the matrix. OF

A: Let's find.

Q: Prove that {4a + 126 : a, b E Z} = {4c: c € Z}.

A:

Q: List all cosets of (([1]3, [2]6)) in Z3 × Ze

A:

Q: 1 a 0 b 1 -1) 31 For which values of a and b is-2 invertible? Why?

A: