2. If the product of matrices cos 0 A = cos O sin 0 cos e sin 0 sin² 0 cos' o B = cos o sin cos o sin o sin? is a null matrix, then e and o differ by (a) an odd multiple of T (b) an even nultiple of n TT (c) an odd multiple of 2 - (d) an even multiple of -

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A: Given: R3×3=cos θ-12sin θ12sin θ12sin θ12+12cos θ12-12cos θ-12sin θ12-12cos θ12+12cos θ To find:…

Q: det a det C

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Q: 1 -2 -1 3 Let A = 4 -3 5 2 1 Let ez be the third column of the 4 x 4 identity matrix I4. Compute Aez…

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Q: sin x COS X [ COS X - sin x

A: Answer and explanation is given below..

Q: 21.1f A' = 34² where A is n by n matrix, then (a) A= 31 (b) A 31 if rank((A) =n () A" =!1 (d) a and…

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Q: dz (b) Determine the by using the Chain rule with the following information: ds z = cos (rªy^) – sin…

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Q: 3. 2 1 1 9. 4 8 For the matrix A 3 -1 %3D 7 8 -1 2 1 1 -2 use Mathematica for find A-1, (b) use…

A: (a) Inverse of the given matrix is evaluated using Mathematica. (b)  A.X=BiPremultiplying A-1 both…

Q: nd a sequence of elementary matrices whose product is the standard matrix for counterclockwise [cos…

A: The standard matrix for counterclockwise rotation through angle  about the origin is

Q: Find the RREF of the matrix 2 3 12 -2 22 -2

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Q: = (3, 6) 2. It is known that u = (-2,3) and v = relative to the inner product in R? which is derived…

A: 2 Given that u=−2,3 and v=3,6 And A=2134. We have to find the u and v. We know that…

Q: Invert the following matrix 3x – 2y = 9 -x + 3y = 3

A: Solution: Consider the given system of equations: 3x - 2y = 9-x + 3y = 3 The coefficient matrix of…

Q: Question -x1 + 3x₂ = 2 2x₁ + x₂ + 4x3 = 3 x2 + 2x3 = 4 [A-¹|I], Find A-¹. (a) Using [IA] (b) Find…

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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: Let A be 3x5 matrix. Then AX=b has always infinitly many solutions.

A: Since not a particular question asked ,as per guidelines solution to first question is given below

Q: aring the Wronskian Matrix and solving it will give cosax sinax W(x)= -asinax acosax sin(ax + b)…

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Q: Assuming that all matrices aren X n and invertible, solve for D. ABC" DBA'C = AB". OD =…

A: Given ABCTDBATC=ABT Also all matrices are nxn and they are invertible which means their inverses…

Q: 3. For each of the following pairs of ordered bases ẞ and ẞ' for P2(R), find the change of…

A: To find the change of coordinates matrix from a basis β′ to β for the vector space VThe identity…

Q: Question 3 [20 marks] I. x + y + 2z = 3 2x + 3y  + 5z= 7 3x + 5y + 7z = 12 a) Write as a matrix…

A: The answer is given as follows:

Q: Let A =mnd B- then the matrix (2AB + A")" is equal to O None of these O equal to the above 2 17

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Q: = = (*) (4) ¹9) 3x 5x-4x

A: Given that fxy=3x-y2x+y and gxy=3x5x-4y. We have to find the matrix A for f∘g.

Q: 10. (a) Show that the matrix is positive definite. (b) Find the square root of A, (A). (c) Write the…

A: In this question, the concept of the matrix is applied. Matrix A matrix is a rectangular array or…

Q: Statement: "Let A and B be n x n matrices, where the columns of A span IR" and B is not equal to the…

A: The given statement is false.

Q: 4 Solve the matrix equation 2X+A=B for X if A= -1 1and B= 2 . X= (Sinpily yr enswi

A: Given: A=-3-4-11-25 & B=1-21-3-4-9 Consider 2x+A=B Since the dimension of the given matrix, A…

Q: Q2)A) If U (x,y)%3DXY-sin n is a function and x,y are function of r,9 defined as follow x =r cos 9 y…

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Q: find the inverse matrix of the matrix

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Q: 3. Express the matrix cos sin 0 B = sin 0 0 cos 0 as a successive proper and improper orthogonal…

A: Given: The matrix is B=cosθ-sinθ0sinθcosθ000-1. To find: The orthogonal transformation. The…

Q: 2 A= 2 4 3 一 1 -2 1 (i) Find A by using cofactor method. (ii1) Find (4) by using adjoint matrix. 19

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Q: Let B = and B' = Find the change of base matrix from B' to B and from B to B'

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Q: Use determinant to find the equation of the line that passes through the points (4, ― 3) & ( ―1,2)

A: We have to find equation of line using given information Concept required: Equation of line passing…

Q: 5. y= e²^(c,cosx+c,sinx)

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Q: Question 20 4 If A is a non-singular matrix whose inverse is 1 A. OD OB O C O A 11 4 2 B. 1 2 4 2 1…

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Q: If the matrix A= [2 5 1;7 3 6;2 5 4], find: A' A(2,3) size(A) LA(:,2)=[] Inv(A)

A: We can solve this as follows:

Q: 2. Find fundamental (3 (a) x' = (b) x' = 2-5 4 matrices for the following systems: :)> (9) -2 62 5 3…

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Q: A = 60- -5 1 0 0 9 2 M33 = A33 = 32

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Q: Find the zeros of Q(x) = 5x - x² + 9 using the quadratic formula. Number of zeros: one

A: Given Quadratic formula is Q(x)=-x2+5x+9 Compare to ax2+bx+c=0 Here a=-1, b=5 and c=9.

Q: (ii) Prove that the product of matrices cos²0 Icos@sin0 cos@sin@] sin?e cos²p B = lcosøsing…

A: Given the matrix is A=cos2θcosθsinθcosθsinθsin2θB=cos2φcosφsinφcosφsinφsin2φ