-2 -11 TO 1 The coordinates [Aleof A= with respect to the basis B= 0 -1 ] 2 of M2x2 O a. -1 -2 O b. 1 1/2 1 -2 -1 3. e. none of these

Q: ove that if AB = 1, then B = A- 2, 1 -1 21 and (b) 3 1 1 1 -2 1 2.

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: [1 2 -3] Find det A A= 4 5 -9 0 1 0]

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Q: |=1|+ |= 2 | |- |- | 3. If z3 + z,, show that VI +

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Q: complex numbers Z1= 4.5-j5.1 , Z2= 3.2- 5.2, Z3= 2.25-j5.6 , Z4= 7.5-j9.2 , then alculate…

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Q: Compute ||w| using w = 6 2 -4 ||w|| = (Type an exact answer, using radicals as needed.)

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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.…

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Q: 1-j 1 Evaluate a. b. 1+j 1+j

A: Given: 1-j1+j Now,  1-j1+j=1-j1+j×1-j1-j=1+j2-2j12-j2=1-1+2j1-(-1)=2j2=j Hence, 1-j1+j=j

Q: . Let 21 2i and z2 = 1+v3i. (a) Express zi and z2 in mod-arg form. (b) Plot in the complex plane the…

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Q: -1 -2 -3 -4- 1 3 Let A = 1 1 1) Compute det (A) using the cofactor expansion along the fi 2) Find…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Consider the calculation

A: Given,                          zN=α,  where N≥1 is an integer and α=|α|ejϕ a nonzero complex…

Q: N(a + bi)N(c + di) = N[(a + bi)(c+ di)] = 2. Show that 65 can be expressed as a sum of two squares…

A: See the detailed solution below.

Q: Let 71 = 3+7i and 72 = 3– 7i and find z172.

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Q: 22 and 21 21 in the form x + iy. 10 + 3i and z2 = 15 – 5i. Find 22 Let z1 - 21 22 22 21 ||

A: Given complex number is

Q: The decimal representation of a positive integer a is given by a = an-1ªn-2 *** α₁α where a =…

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Q: 1. 4 -2 3 Compute A- 513 and (51 )A, where A = -4 4 -7 3 1 A-513 = %3D (513)A =

A: To find - Compute A - 5I3, and 5I3A, where A = 4-23-44-7-311

Q: You are given that B = {1 – x², 1+ x, 2x + 3x²} is a basis for P2 and - 2 [p(x)]B= |3. If p(x) = a +…

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Q: 11. For what value(s) of k does the following set of vectors form a basis for R³? ·4·0 3 3

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Q: Determine all minors and cofactors of [9 3 A = 5 9 9. M = 9. C = 9.

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Q: 41 1 -1 -8- 1 3. -2 Find the basis for the column space of -2 -6 4 a. {0 C. a 3. b. { d. {-1

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Q: 1 0 5 1 1 0 -1 3 A = -1 1 B =| 4 4 -1 -1 -2 3 2 3 1 3

A: To find The trace of the given matrix.

Q: 0,1,0) R3 Ba

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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: 7,Prove the following fact: for any two positive integer a and b, gcd(2ª – 1, 2° – 1) = 29cd(a,b)–1.…

A: The question has a typo. It should be gcd(2^a -1, 2^b-1)=2^(gcd(a,b))-1. The -1 is not in the power.…

Q: 0555 if A = 0 0 0 0 then the basis fqf 0 205 N(A") is 1 .a Hạmmad Selawe .b كواے 1 .c 0.

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Q: ?:R3 →R2,with? ?,?,? =(?+2?+3?,4?+?−2?) Find a basis for the image and state its dimension.

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Q: 4) Let z= 1+ V 3 i. Compute all values of z". Exponential notation is sufficient. Sketch these…

A: Given: z=1+3i

Q: (a) Find the left cosets of {e, (1, 2)} in S3. (b) Find the right cosets of {e, (1, 2)} in S3.

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Q: ow that postage 6 cel using or imps. (Consider the basis step for 6 and 7 cents, and the generic…

A: Given that postage of 6 cents or more can be achieved by using only 2-cent and 7-cent stamps.

Q: 31 Let A =-1 4 and B = 3] 2 [3 -1 . Compute the (3, 1) entry of AB.

A: Given: A=23−1403  and  B=3−13124[AB](3,2)=?[AB](2,3)=?

Q: Verify that (AB) = BTAT. 6 1-1 Find (AB)T. 11 0 -20 X Find BTAT. 11 A = 0 1 30 0 -20 6 9 43 6 9 43 →…

A: A=61-1018306 and B=10-161-6018. To Do: Verify ABT=BTAT.

Q: 1 a) Let A =-1 [1 0 3 and C =2 1 l1 31 [1 2 1 1 B = 2 2 1 If possible, -2 1] li 3 -1] 1 compute (A"…

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Q: Compute w using w= 7 - 3 ||w|| = (Type an exact answer, using radicals a

A: We have to find .

Q: Find JA|, IB|, A + B, and |A + BỊ. Then verify that |A| + |B| # |A + B|. 15 0 1 -1 A = 1 -1 0 B = 5…

A: topic - determinant and matrices

Q: Question 1. (a) Prove that for z, w = C, Re (zw) = |z||w| if and only if z = sw for some positive…

A: a)  suppose that the complex numbers are   z=a+ib and w=c+id .  Then we see that w¯= c-id  we see…

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.