(31/1/2 03 A= 1 1 - 1 3 3 3 1 0 0 0 0 0 0 0 -130 0 0 10 3/

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: This is a linear algebra question Suppose A is a square matrix with Col(A) is a subset of Null(A).…

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Q: Show that the following set is convex: with A € ST C₁ = {x R¹|x Ax ≤ 1},

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Q: Find f(B)

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Q: For matrix (0 -1 0, 1 0 0, 0 0 1), show that [adj(A)}^-1 = (1 / det(A))*A = adj (A^-1)

A: The objective of the question is to prove the identity adj(A)^-1 = (1 / det(A))*A = adj (A^-1) for…

Q: True or False? Justify your answer. a) Let A, B, and C be two square matrices of the same dimension…

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Q: t A be the square matrix (abcd) A. If ad−bc = 1, then show that A^−1 =(d−b−ca ) B. If ad−bc=α, then…

A: If  is a square matrix then its inverse is where

Q: Given the matrix      A=       [4 -1   0   2] , then the trace of A^3 is?

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Q: S)Give an example of a matrix A such that A2 = I but A#I or A± -I.

A: There are so many examples.

Q: Given A = 1 0 0 -3 1 1 1 - 2 -1 " x = and b = 300 150 400

A: Given that the system Ax=bHere A=1-3101-201-1 , b=300150400

Q: * Find the Matrix B from order 2 x 4 , Its elements are written in the form by = i + ()

A: Here we find matrix B of order 2×4

Q: -9 4 4 1. Let A = -8 3 4 . Find an invertible matrix P and diagonal matrix D so that A = PDP-1.…

A: See the detailed solution below.

Q: Determine the matrix A x 1, if A=(13) and 1=(9)=

A: Given A=-1043,     I=1001   To determine: the matrix A×I

Q: Let A = [0 1 0 0 ], A^(-1) is equal to: * Does not exist Identity matrix Null matrix

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Q: Find an example of a 2 x 2 matrix A such that A? + I2, A3 + I2, and A6 = I2. Explain how you know,…

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Q: Determine whether the following matrix is invertible by finding its determinant. 4 -14 -56

A: Consider the matrix 14-14-56

Q: Let A = (2 1, 2 3) . Find a 2 x2 matrix X so that X^2 = A

A: Matrix A =[2 1, 2 3]  We have to find 2*2 matrix X such that X2=A

Q: what is the x on this matrix; Ax(D+Bx)^-1 = C

A: Using matrix multiplication,

Q: For a non-singular matrix A, A^(-1) is equal to: (adj(A)) / det(A) det(A) x (adj(A)) det(A) x A

A: Explained below

Q: Show that (-A) T= -A", where A is a 2x3 type matrix (you can show it on the example)

A: Let matrix A=abcdef. Order of matrix A is 2×3. ⇒-A=-a-b-c-d-e-f ⇒(-A)T=-a-d-b-e-c-f  →Result 1

Q: 4. Let A be a symmetric matrix. Show that (A' + A) is symmetric.

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Q: Find matrix B such that AB = C. Hint: B = A^-1 x C *

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Q: Let A be a 4x4 matrix and det(A)=2. Find det(2A-)'

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