(a) Let A, B be n × n symmetric matrices such that XTAX = X™BX for all column vectors X e R". Show that A = B.

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: M2,2 is the vector space of all 2 x 2 matrices. List the o element of this vector space.

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Q: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

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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: 5) Give an example of matrices D and F where DF is defined, but FD is not, and clearly explain why…

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Q: a) For invertible matrices A, BE R™×", show that ((AB)")-1 = (A-1)" (B1)". b) Let A, B, C, D e R"*"…

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Q: find a matrix that column space is spanned by fewer vectors than there are columns in the matrix

A: The idea is the create a matrix such that one of the columns is in the linear span of the other two…

Q: Find the charo cteristica poly no nomi the matrix A = 3. 3. /- P(x) = 1.

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Q: Let a € R, and define vectors u₁, U2, U3 € R³ in terms of a by E] 2 U₂ = a U₁ = 3a +3 2a +3 a² + 3a]…

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Q: Let A be a 2 by 7 matrix. Then -A is aby_matrix, and A is a-by-matrix.

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Q: Write a second degree equation matrix and prove that it is in vector space?

A: To show: An example of a second-degree equation matrix which is in vector space.

Q: do

A: As per our guidelines only first three sub questions are solved. For remaining sub questions kindly…

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: Draw the set of all two-dimensional vectors whose 1-norm is equal to 2. For the matrix 7 A = -2…

A: Given: A=700-2

Q: Does the set of all 2x2 matrices form a vector space, please explain.

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Q: Let A = [kaij]nxn, B = [aij]nxn, be an nxn matrices and k be a scalar then det(A) is equal to: *…

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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: Write y as the sum of a vector

A: Given,   And

Q: (a) Consider the system of equations 11х3 — Зх1 yi %3D - 7x1 – 6x2 – 5x3 y2 х> + 2х3 — 2х = y3…

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Q: Determine whether the span of the column vectors of the given matrix A is equal to R^3. Show your…

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Q: image1

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Q: Show that a triangular matrix is normal if it is diagonal

A: Given: A triangular matrix is normal.if it is diagonal

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.