If Q = I - auu" where Qis an orthogonal matrix, a > 0, and u E R"X1 real vector, and I is n x n identity matrix then a. a = 2

Q: a) Prove the following: a+b a a a+b =b° (3a +b) a a a a+b

A: Since you have posted more than one question, we solve the first one for you. For the other…

Q: Let C be an nxn matrix that satisfies C2 -3C–2In 0. Show that C is invertible and C=1 = }(31-A)

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Q: B) Suppose A is an invertible matrix inM, (R). And x, y E R". Prove it: det(A+ ry") = (1+y"…

A: Given: A is an invertible matrix in Mn(ℝ) x,y∈ℝn To prove: det(A+xyT)=(I+yTA-1x)det(A)

Q: and = %3D are oignualus of a matrix A Corraspondeng to the egnualuong=2 and >=-2 then = ACTa t Ja)=…

A: For a given matrix A if 'x' is eigen vector of matrix A corresponding to the eigen value ' q ' then…

Q: rewrite ax^2+by^2+cz^2+dxy+exz+fyz+gx+hy+iz+j=0 in  standard form by matrix

A: The objective of the question is to rewrite the given quadratic equation in three variables in…

Q: ) If the matrix A= [4 2 1; 1 5 9; 3 8 7], find: · A' - A(3,1) - size(A) - A(:,2)= [] Inv(A)

A: Since, you have posted a question with multiple sub-parts, as per company policy we will solve first…

Q: Let y = a. UTU= UUT 8 4 = II a. Let U be the 2 x 1 matrix whose only column is u₁. Compute UTU and…

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Q: If A,B,C are nxn invertible matrices and I is nxn unit matrix C-(A + X)B¬1 = I What is the solution…

A: Given that C-1(A+X)B-1=I   To Find: X=?…

Q: A)  Justify if the matrix A is diagonalizable.B)  Find a matrix T and a diagonal matrix J, such that…

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Q: Consider matrix attatched and vectors attatched, Let w = Ax+y. Write down w2.

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Q: QUESTION 2. than one statement may be true Which of the following statements are true? Note that…

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Q: 13. A and B are two square matrices of the same dimension. We are given that Aw = 5w and Bw=3w.…

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Q: Suppose A is the 3 by 3 matrix ones (3,3) of all ones. Find two independent vec- tors and y that…

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Q: 1. For any matrices A, B, and C of appropriate sizes, show that if C and A = A-BC-'B" are…

A: we have, matrices A, B and C of appropriate sizes, By definition of invertibility of matrices , we…

Q: Which one of the following equations is true for nxn matrices A, B, and C? (Assume all matrices…

A: For the given matrices A, B, and C. We have to choose the correct option.

Q: 8. A matrix A is augmented with a vector b-(bi, bz, b). After applying Gaussian elimination to the…

A: Solve the following

Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

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Q: Q/ Let A: am et fox)= 2x- 子 4x+5 whene I Find FCA) is unit matrix

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Q: 1) Determine whether the given vectors are linearly dependent or linearly independent. a)…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 2 -2/2 2/2 , show that A and B satisfy 2 Q#5: If A= and B 2 commutative property with respect matrix…

A: Given  A=2-2222  and  B=222-22. We have to show that  AB=BA.

Q: If Q = I- auu' where Qis an orthogonal matrix, a > 0, and u e R"x1 real vector, and I is n x n…

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Q: (2) Decide whether the given statement is true of false. Prove your answer. i) If Az = Bx for some…

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Q: Part 1: Find the inverse of the matrix A, if it exists. A 033 -4 03 o] 060 06

A: The matrix is: A=033-403060 To Do: We have to find the inverse of the matrix if it exists.   Note-…

Q: 1. Consider the matrix and and Monde Cole 2022 202) Mesh Colleg 202C) Mona that 1 1 0 101 0 1 1 Mo…

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Q: If A, B, C and D are invertible matrices of same size such that DCBA(BA)-'C-'(C-'D)-' = DA='C². %3D…

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Q: 4 [1] 2. Is the vector 5 in the column space of matrix A = 1 0 -2 −4 4 4 5 3 -13]

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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: b) Let A = Bar = and A¹C = B. Find a matrix X such that X = AC.

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Q: Find a and that solve the vector equation: a) α (²)+(¹²) = (19) Suppose the above equation is…

A: System of linear equations

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Q: and ß that solve the vector equation: a (²) + ( )= (²²) (21) B 3 28

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Q: Let A, B, C and D be invertible n xn matrices with n> 7, which satisfy the equation ABCT DBA"C = ABT…

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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.