Let B = {(1, 1), (2, 3)} and B′ = {(5, 2), (1, 3)} be two bases for R2. [T]B= 2 3 4 7 (a) Find (T (v))B′ , where (v)B′ = (2, −1). (b) Verify your answer in (a).

Q: Are the following two sets of coefficients orthogonal? -1, 0, 0, 1 -1, 1, 0, 0 Yes No

A: Given data is as follows: -1,0,0,1 -1,1,0,0 Yes the following sets of coefficients are orthogonal as…

Q: Find AB such that [3 1 21 T-1 A = 2 1 2 and B =|4 [1 2 2] -2 -5]

A: The solution is given as

Q: c. Find the coordinate vector of the polynomial q(t)=3t² − 6t+2, relative to the basis for P₂ in…

A:

Q: (a) 2+j - j(x+jy) メ=? y-? 1-j (b) (2+j)(3-j2) = a+jb a=? be? ((メ-j2y) -(y-Jx)-2) x? y?

A:

Q: Use proof by contradiction approach to prove that VxM) V N(X)

A: This is a problem of Predicate Logic.

Q: (a) Find the constants A, B, C, and D that satisfy 1 1 1+ (w/o)² 1 + ((z-w)/7)2 Aw B Cw D 1+ (w/o)²…

A: Use partial fractions

Q: Let a = (1,2, 3), b = (1,0, –1) and c = (2, 1, 3). (a) Verify that a · (2 b+c) =2(a · b) + (a · c).

A: a=(1,2,3) , b=(1,0,-1) and c=(2,1,3)

Q: Show that (u×v)· w = u ·(v×w).

A: As we know that, Multiplication is an Associative Property, i.e. (a x b).c=a.(b x c) and Sometimes…

Q: Find the L(e2" (1+ t)²). ,2t a) + (s-2)* 1 b) + (s-2)2 2 (s-2)3 (s-2)2 c)+2 (s+2)³ (s-2)? d) +…

A: The following formulas can be used to obtain the Laplace transform.…

Q: Find JA|, |B|, A + B, and |A + BỊ. Then verify that |A| + |B| # |A 1 6 [o 1 -1 A = 1 -1 0 B = 6 1 1.…

A:

Q: Q1: Sketch the signals A. x(t) x(-1/2) A CL x(2(1+2)) x(−1+1) Ates Ades 0 2 B. 2 x(t) 0 1 x (3t),…

A: Given data:- Part A=   Part B

Q: vx(A x s) = (B · v) A - (a.o)o +a (v-t) – 3 (v. A) %3D

A:

Q: Derive the expression F1− F2 = (F1 − Fc)[exp( f φ) − 1/exp( f φ)] using the equation (F1− Fc/F2−…

A: Given efφ=F1-Fc/F2-Fc=F1F2-Fc-F2FcF2 1efφ=F2F1F2-Fc-F2Fc Now…

Q: 6 - 1 2 Compute A - 31I, and (312 )A, where A = - 5 4 - 5 - 3 1 2

A:

Q: Evaluate f (x + y - z)² dV for the box B with dimension: [0, 8] × [0, 7] × [0, 3]. B (Use symbolic…

A:

Q: (a) [1 2]. [–1 1] (c) [1 3], [2 – 3]. [0 2] (d) [2 4], [-1 2] (b) [0 0]. [1 1]. [–2 – 2]

A:

Q: Show that (0, 1) ~ R.

A: We need to show that the open interval (0, 1) and R( the set of real numbers) are equivalents. The…

Q: Let a bc A= d ef g hi Assuming that det(A) = – 7, find a) Det(2A) b) Det(A´') c) Det(3A') d)…

A: Given that: A=abcdefghiand det(A)=-7

Q: Express in the form of x + iy: 6-7i (i) 5+i 1 + (3+i)2 1 (ii) (3-i)2

A:

Q: Derive the expression  F1− F2 = (F1 − Fc)exp( f φ) − 1/exp( f φ) using the equation (F1− Fc/F2− Fc)=…

A: Given that, F1− FcF2− Fc= efφ To derive F1-F2=F1 − Fcefφ-1efφ. Consider, F1− FcF2− Fc= efφ Then,…

Q: Prove that bx q = b. ((Vt) - Vt), where q = V x t

A: We have to prove b→×q→=b→·∇t→Tr-∇t→ for q→=∇×t→ b→×q→=b→×∇×t→          =b→×∑i^∂∂ti×t→…

Q: Given Ā =, B =,č = (a) Compute Ā· (B + T) (b) Compute A · (B × C)

A:

Q: Prove Equationally that A → BF¬B → ¬A.

A: let us check whether the given statement is true or not

Q: If Z1 = 4 + 5i and Z 2 = -1 + I,  express in the form a + bi  (i) Z1 + Z2   (ii) Z1 – Z2

A: Formula used  sum of two complex number is given by  (a1+b1i)+(a2+b2i)=(a1+a2)+i(b1+b2)

Q: Determine the main base function as one of f(x) = x, f(x) =x², f(x) = Vx , or f(x) = -. 1 а) h(x) —…

A: A)h(x)=x-7The function h(x) is obtained byvertical transformations of 7 units downof f(x)=xThe base…

Q: Using the substitution u = (A) (B) C D 1+1 du [₁ -1/2 du [(u ¹/2 - u-1/2) d du (u - 1) / u-²1) x + 1…

A:

Q: y'sec*xdx – (1– 2y'tanx)dy = 0

A: We solve the given DE  y3sec2xdx-(1-2y2tanx)dy=0.......(1)

Q: Verify that (AB)T = BTAT.

A:

Q: Which one of the following is isomorphic to Z4 x Z6/((2,4))?

A:

Q: Let A = {a, b}, B = {x, y}, C = {x, z}. а) (6.1 #32b) Find P(A x B). a

A:

Q: Prove that: ^ ( a ) 2 ² 1 ( ² + ²; ; ; ; ; x ² ) = ↓ sin¯' x } 3 + 2² (¹-²)=an (b) 1 ¹ tan^¹ x ܐ

A:

Q: 3. Find all real numbers t for V = (20 t,4t - 4,5t², t²) are orthogonal. - which = (1,5t,-4t, t³)…

A:

Q: d) w. (w x v) = e) w x w = (?, ?, ?) f) (6v2u) × (6v - 2u) = (?, ?, ?)

A: Given query is to perform indicated vector operation.

Q: T: ([₂]) = 3x1 +4x2 x1 - 2x2 4x1

A:

Q: ³₁(1+w) (2w + w²)5 dw

A:

Q: Find |A|, [B], A + B, and JA + BỊ. Then verify that |A| + |B| = |A + BỊ. 1 7 A = 1 -1 0 0 1 -1 B = 7…

A: We can solve this as follows:

Q: Prove that (b − proja (b)) · a = 0.

A:

Q: Consider z1 = 1 - j2 and z2 = -2 + j3. Determine Im (21)?

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.