If A is 3 x 3 matrix such that (A + I3)² = 0 %3D Show that: A is invertible.

Q: Suppose (B-C)D=0, where B and C are mxn matrices and D is invertible. Show that B = C.

A: The given matrix equation is B-CD=0 B and C are the matrices of the order m×n while D is the…

Q: 9. A = -2 2

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Q: let Q(x)= x12 -8x1x2 -5x22 , then matrix A of the quadratic from is A=?

A: Explanation is given below..

Q: Suppose that A and B are invertible 2 x 2 matrices such that det(AT) = 2 and det(B) = -2. Let x ER…

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Q: For which value of x is the following matrix not invertible: 1 1 2x A = 1 2x 2x 2x 2x 2x 4 1 -1 1 2

A: For a matrix A to not be invertible: dat(A) = 0.

Q: Find the characteristics roots of the matrix 2 A =| 1 2. 2.

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Q: Let A is a 4 x 4 matrix such that Ar=0 has non trivial solutions. Is the matrix A invertible?…

A: If the equation Ax = 0 has non-trivial solutions, the matrix A is not invertible.Explanation:Steps…

Q: b) Evaluate det[(2A)-1 (3A")], where A is any invertible (2 x 2) matrix.

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Q: Find a 3 × 2 matrix A and has LU factorization where L is diagonal.

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Q: Give an example of a 2 x 3 matrix A that is in RREF and whose solutions to 2 -(-) 4 Ax = 0 is…

A: Introduction: Systems of linear equations can be solved using a type of matrix called reduced row…

Q: Consider the matrix B given by 0 0 0 B = 1 0 0 0 1 0 Show that B3 = 0. Also, compute for the product…

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Q: Give an example of a 3 x 3 matrix A such that Nul(A) # {0}.

A: Let T:ℝ3→ℝ3 be a linear transformation defined by T(x,y,z)=x-y,y-z,z-x Therefore Ker T=x,y,z∈R3:…

Q: If A is 4 by 4 and invertible, describe the nullspace of the 4 by 8 matrix B = [ A A].

A: Given that A is 4×4 and invertible matrix. To describe the null space of the 4×8 matrix B=AA. Null…

Q: If A is an nxn invertible matrix, then Select one: -1 a. A"= det(A)/adj(A) -1 b. A"=…

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

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Q: Consider the following matrix. Show that Col(B) and Null(B^T) are orthogonal to each other.

A: Step 1: Step 2: Step 3: Step 4:

Q: 2 Consider the 3 × 3 matrix B = 1 2h -1 1 2 1

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