O Mark the following either true or false. Justification is required. For square matrix A, det (A) = det (AT). A row replacement operation changes the sign of the deter- minant of the matrix. • In general, for nxn matrices A and B, det (AB) ‡ det A det B.

Q: B. Express the ff atticher whit with general Form quadortic function. 1. 2 9=C++3) ²-3 FLAMU

A: The general form of a quadratic function is

Q: 1. Write down the geodesic equations in the Schwarzschild geometry in Schwarzschild co- ordinates…

A:

Q: Let V be the vector space of symmetric 2 x 2 matrices and W be the subspace W-spand W = span{ a.…

A: We need to find two elements X and Y.

Q: Use the binomial expansion to find the order of the following ex- pressions as x → 0. x3/2

A:

Q: Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is…

A:

Q: (7) Let m≥ 1 and let R= {0, 1, 2,...,m - 1}. (a) Prove that if r1, T2 € R and r₁ r2 (mod m), then r₁…

A:

Q: For any set A, both Ø and A are in the power set (A).

A: The power set P(A) of a set A is the set of all possible subsets of A, including the empty set (∅)…

Q: y" + y = secx tan x

A:

Q: d²x dt² solve for x. 2 + w³²x = F sin wt

A: Given differential equation isd2X/dt2  + w2X = F0 sinwt

Q: 1 Find the inverse of the matrix, if it exists. Use the algorithm for finding A by row reducing [A…

A:

Q: 5. Let V = {ax¹ + (b − c)x² + 3ax +c+2b: a, b, c ≤ R} ≤ P4. Construct an isomorphism from V to R³.…

A: Given vector space is So we have So  ,  So basis for the vector space  is  .Hence  .Noted that if…

Q: 15. Derive the Newton's method for finding the qth root of a positive number N, N¹/9, where N > 0,…

A:

Q: Use the Theorem of Pappus to find the volume of the given solid. the solid obtained by rotating the…

A:

Q: Let p be a prime number. Prove that Z/pZ is a field.

A: Let R be a commutative ring with unity. Then an ideal M of R is maximal if and only if the quotient…

Q: Pivot once as indicated in the given simplex cableau. Read the solution from the result. Pivot…

A:

Q: Expand the given set to form a basis for R³. (IC) BO

A: Given set  We have to expand the basis for

Q: dy Find eigenvalues & eigenvectors. = [²:2] Y dt 3-2

A:

Q: Find the limit x lim (1.3) (0,0) 2¹+ y² + y8

A:

Q: Let L₁ be the line passing through the points Q₁=(4, -2,-4) and Q₂=(3, 1, -7) and let L₂ be the line…

A:

Q: It is not always possible to construct by ruler and compass, a square equal in area to the area

A: We have to show that It is not always possible to construct by ruler and compass, a square equal in…

Q: 1. Consider the following function, sin 1(2) - (2²46² (²) ƒ(x): if x = 0 if x = 0 Prove that the…

A: A function f is termed differentiable at a point x=a if the limit f′(a)=limh→0f(a+h)−f(a)h exists.…

Q: Which of the following would best represent the statement "the plane is flying to the left of me,…

A: Which of the following would best represent the statement "the plane flying to the left of me, but…

Q: Find the particular solution of the differential equation x²y" + 8xy' +12y = 1x 4 y'(1) = 42.…

A: We have to solve the differential equation.

Q: 18. Determine which of the following functions are one-to-one and which are onto. If the function is…

A:

Q: The function ƒ is defined by ƒ (x) = x³ – 5 sin (2x). Find all values of a that satisfy the…

A:

Q: 4. (i) For an odd number n, suppose that 2" # 2 mod n. Can n be a prime? Explain. This is called the…

A: Eulers and fermats little theorem will used

Q: Solve the following Non-Exact Differential equations and find its integrating factor. 1. xy² dx +…

A:

Q: you want. 1. Prove that the sequence an converges. The sequence is defined by ao = Task 2. Let an be…

A:

Q: and if f(x) = sin" (x²) Lim 0 find 2m + n f(x) f'(x) (1 − cos x)m - = 2√√√3

A: Given that                                                            Formula:…

Q: 24.6 Let fn(x) = (x − 1)² for x = [0, 1]. (a) Does the sequence (fn) converge pointwise on the set…

A:

Q: ſőt, dt + f(2 − t), dt

A:

Q: (a)Suppose that f is an injection. Show that f -1∘f(x) = x for all x∊D(f) and that f∘f -1(y)=y for…

A:

Q: Which set of values for x should be tested to determine the possible zeros of 2x³ - 3x² + 3x - 10? O…

A:

Q: Use the eighteen rules of inference to derive the conclusions of the symbolized argument below. B D…

A: The objective is to prove the given argument using rules of inference.

Q: Let S be a nonempty subset of R that is bounded below. Prove that inf S= -sup{-s:s∊S}

A:

Q: 1. 2. n−1 4 nh+n-6 7n+1 n² +1

A: We shall divide and using the highest power of n and then find the limit

Q: 1. Find the Taylor or Laurent expansion of the following functions at zo = 1 Z (1) z²-2z+5² (2) Z…

A:

Q: Suppose you have a value (g = 23) in the field F79. Without computing any powers of g or any…

A:

Q: 2) A) If x= Sup S, show using the definition of supremum that for each ε>0, there is an element aes…

A:

Q: 3. Use the definition of a convex set to show that if S₁ and S₂ are convex sets in R+", then so is…

A:

Q: 20.2 Solve the following linear congruences: (i) 341x = 15 mod 912; (ii) 341x = 15 mod 913; (iii)…

A: To solve the linear congruence , you can use the extended Euclidean algorithm to find the modular…

Q: Find the orthogonal projection of y = W = Span U₁ = -2 3 Ex: 1.23 112 = 0 []} onto the subspace

A:

Q: Suppose the function y = h(x) is nonnegative and continuous on (a.B), which implies that the area…

A:

Q: Let be a family of sets and let B E . Prove that BC UAE A. Proof. Let E B. Define A = [Select] so…

A:

Q: XA = In the figure shown below, the coordinates of A and B are known with values x₁ = 100.00m, YA =…

A:

Q: the differential equation that describes the motion.

A: Spring constant k=8g/s2 and the mass stretched the spring by,  l=245 cmThe damping coefficient…

Q: 3. 4. For the function y = A sin(B(x − C′) ) – D, which variable determines amplitude? A b. B C. с…

A:

Q: The supply and demand equations of two interdependent commodities are Qs, = 4(P₁-1)-5. Qs₂ = P₁ -3.…

A:

Q: Show that if f: A→B and E, F are subsets of A then f(E∪F) = f(E)∪f(F) and f(E∩F) ⊆ f(E)∩f(F).

A:

Q: Beulah and Biff invest in Bertha Fund. They make an initial deposit of $1,000. After 1 year they…

A: