Suppose that A is a 3×3 matrix and det (A) = -4. What is det (4A)?

Q: [5] Find three different 2 by 2 matrices that have A₁ = A₂ = 0.

A: Three different 2×2 matrices that have λ1=λ2=0 i.e, both eigen values are 0 are 0100,0020 and -4-284

Q: 1. Let, A = -1 21 Find the matrix -5A3 + 2A? + 4A + 512. 9 21

A: Given: A=-1292 Determine A3. A3=-1292-1292-1292=192922-1292=-14218962

Q: Give an example of a 4 x 4 matrix that is symmetric, has with the (2,4)-entry equal to -5, and has…

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Q: -2 6. What is the diagonal matrix Find an orthogonal matrix Q that diagonalizes A = 6. A?

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Q: Ei) dim(COLA) is (ii) dim(ColA)- is (ii) dim(RowA) is (iv) dim(RowA)- is (v) dim(NulA) is

A:

Q: t matrix B= 5-21 4-2 what is The 2. 3. 1-12 -12 reduced Yow echelon form of 6 B.

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Q: 4x+5y+4z = 8 3x+3y+ z =-9 5x+5y+2z = -1 Write the augmented matrix:

A: For a system of equations is a matrix of numbers in which each row represents the constants from one…

Q: Demonstrate that A A-1 = A-1 A = I

A:

Q: Suppose A is a 8x4 matrix such that rank(A) = 3. Find dim(col(A)-). dim(col(A)+) =

A: To find: dimcol(A)⊥ Given information: A is 8×4 matrix such that rank(A)=3. Concept used:…

Q: What is the rank of the matrix A = 2 1 5 -1 2 -5 0 3? -3

A: See this solution in below.

Q: Let A, B and C be invertible, nxn matrices with AB BA and I, the n x n identity matrix. If AXB-= I+…

A: Invertible Matrix: An invertible matrix is a matrix for which matrix inversion operation exists,…

Q: Evaluate det (A) for the matrix A=($ 2).

A: Given matrix is A=8254 The task is to find the inverse of the given matrix.

Q: 3. Tell whether the statement is true or false. If true, provide a proof. If false, provide a…

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Q: Suppose that B is a square matrix with det(B) = -2. Find each of the following. (a) det(B6) = (b)…

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Q: (18) Does a 2 × 2 diagonal matrix commute with every other 2 × 2 matrix?

A: We have to check

Q: Compute the adjugate of the following matrix: -7 3 -6 0 0 0 0 0 0 0 0 0 adj -7 0 -2 %3D | 2 -8 4

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Q: Q1 (d): Find the rank of the matrix A. 1 0 5 0 1 -2 2 -2 -1 1 -6 3 -2 12 2 -3 0 2

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Q: Find an invertible matrix X and a diagonal matrix D such that X-1 AX = D. You don't need to compute…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: If A is a 3 x3 matrix and det(A) =-3, what is det(4A)?

A:

Q: Suppose A is a square matrix. Show (a) A+A" is symmetric, (b) A – A" is skew-symmetric, (c) A= B+ C,…

A: Sum of symmetric and skew-symmetric matrix is matrix it self. Like for matrix A, Symmetric matrix =…

Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

Q: If a matrix A is such that, 3A³ + 2A² + 5A + I = 0 then its inverse is?

A:

Q: Find a 2 × 2 matrix that maps e₁ to -3e2 and e2 to 2e1–e2.

A: The 2x2 matrix that maps e1 to -3e2 and e2 to 2e1 - e2 is [02​−3−1​]Explanation:

Q: Diagonalize the matrix [5 -14] 4 -10 A = by writing it as A = PDP-¹ P = D = P-1 =

A:

Q: for a matrix A 3 6 2 5 if f(x)=(x+2)(x-2), calculate f(A)

A: Given: Matrix A=3625 To Find: f(A) when f(x)=(x+2)(x-2)

Q: If A is an m x p matrix and B is a p x n matrix, then their product AB will be?

A: Two matrix can only be miltiplied if number of column of first matrix is equal to number of row of…

Q: Give an example of a 3 × 3 matrix with real inputs that is not similar to a matrix diagonal

A: A matrix is said to be a diagonalisable  if it is similar to a diagonal matrix. Therefore we need to…

Q: Find 2A-l if we have the matrix 2 1

A: A=32102A=232102A=2×32×22×12×02A=6420

Q: If matrix [A] is a 5x5 matrix and a matrix [Z] is obtained by the row operations of replacing Rowl…

A: .

Q: Let A be a nonsingular 4×4 matrix with det(A¯1) = - 2 Then det(2adj(A)) 1 8 -2 4 -1 8 None -4

A: Use the properties of the matrix to solve the problem.

Q: Find all values of a such that A3 = 2A, where   (see image of matrix)

A: Consider the given matrix,

Q: Explain why det (BPB¯¹) = det(P) for any matrices P and B. Assume both sides of the equation are…

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Q: Find the matrix B such that 2AT+3B=0.

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Q: Since Matrix A is not a square matrix, doesn't that mean that it won't have an inverse?

A: A=1111-11B=0.250.250.5-0.50.250.25