Given the matrix 24 -34 A = 13 -18 Find an invertible matrix P such that C = P-'AP is a matrix of the form where a and b are nonnegative real numbers. Write down the matrix C explicitly.

Q: a) If a 7 × 5 Matrix A has rank 2, find dim(Null A), dim (Row A) and rank AT

A: 1) Given  7×5 matrix  rank(A)=2 using rank nullity theorem we have rank A + null A= number of…

Q: 1. Find the cofgctor of 6 in matrix B. 4 り り

A: We will find out the cofactor of 6 for given matrix B.

Q: Find the characteristic equation of the matrix by inspection. 4 2] -6 0 0 6 0 0 5] 4 -9 LO

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Q: Consider an 5 x 5 matrix A satisfying the following two properties: (a) Every row has exactly one…

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Q: Find an SVD of the matrix. -7 3 A = - 3 - 1 O (Type an exact answer, using radicals as needed.) A =

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Q: Find a matrix A such that e [-] -2 is a solution for Ax= x'.

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Q: [3 Compute the natrix exponential e4t for the diagonal matrix A = !!

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Q: If a 6 x3 matrix A has rank 3, find nullity A, rank A, and rank AT. nullity A = rank A= rank AT=

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Q: 6. Suppose  X + XB = C, where X, B, and C are square matrices of the same size. a.  Derive an…

A: We will see that (I+B) must be invertible for existence of X.

Q: 2) An n x n matrix A is called nilpotent if Ak = 0 for some positive integer k. Show that if A + 0…

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Q: Consider the following matrix A, where 0 -4 -6 0 -3 A = -1 1 2 5 Find an invertible matrix P and a…

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Q: 3. Let A [1.1 -0.1] [0.3 0.7 0.7] Is matrix A invertible? How do you know?

A: An invertible matric is a matrix  for which matrix inversion operation exists . A matrix is said to…

Q: Given a particular matrix A and a vector x + 0, discuss how to determine whether x is an eigenvector…

A: Let A is any matrix of order n×n. The scalar λ is an eigen value of A when there is non zero vector…

Q: 6. Show that if Q is an orthogonal matrix, then 1 0 %3D 0 Q is also an orthogonal matrix.

A: We have to show that HHt = I

Q: Find an SVD of the matrix. – 6 -5 A = A=

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Q: If A is 3 x 3 matrix such that A 2 then A is -4 diagonalizable. Select one: True False 1 1224

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Q: Suppose A is a matrix such that A² + A = I, I is the identity matrix. Show that a) A must be square.…

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Q: A matrix A is similar to matrix B, if for some invertible matrix P, B = P''AP. Is B similar to A?

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Q: Consider the matrix A given by 4. -5 3 6 -6 6 5 A = 9 3 -3 0 2 -4 Using elimination, find a lower…

A: LU decomposition of the matrix

Q: 1. Find an example of a 2 x 2 matrix A such that A² # I2, A³ + I2, and A® = I2. Explain how you…

A: Given that  a 2×2 matrix A such that A2≠I2,  A3≠I2 and  A6=I2

Q: Find a 3 x 1 matrix x with entries not all zero such that 1 2 -1 Ax = 1x, where A 1 1 -4

A: A=1  2-11  0  14-4  5 Now let x=abc be the required matrix. Now consider, Ax=1x⇒1  2-11  0  14-4…

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: 2) If IAI = 3, where A is a 3x3 matrix, caleulate the folowing: 2a) det ( ZA) 26) det (A) 2c) det (…

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Q: 1. Show that the matrix 2 1 A = 1 2 -1 -1 is positive definite.

A: Given :- a matrix A  We need to show that a matrix is positive definite. We know that , A symmetric…

Q: 4 9- That is, find an -5. | Diagonalize the matrix A [3 invertible matrix P and a diagonal matrix D…

A: Given matrix A=4-63-5

Q: Show that if A is nilpotent, then I-A is invertible. A square matrix A is nilpotent of index k when…

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Q: FInd the Solution by Considering Attachment.

A: The method of mathematical induction can be followed to prove above result. Now, The given matrix is…

Q: Consider A = 21 2 1 3 -1 -3 4 Convert A to an upper triangular matrix U by using Gaussian…

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Q: A matrix A is similar to matrix B, if for some invertible matrix P, B = P''AP. Prove that if A is…

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Q: Show that the matrix A = singular. 1 -2 3 4 0 5 0 is 60

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Q: 1. Find an example of a 2 x 2 matrix A such that A? + I2, A3 + I2, and A6 = I2. Explain how you…

A: Given A3≠I2,A2≠I2and A6=I2

Q: Let E be the elementary 3 x 3 matrix corresponding to the elementary row operation of multiplying…

A: Elementary matrices: Elementary matrices are n×n square matrix which is obtained performing…

Q: If A be a (n × n) invertible matrix the prove that the Ax = b has exactly one solution.

A: Given- The matrix A be a n×n invertible matrix. To prove- That the Ax=b has exatly oly one solution.…

Q: Show that if a square matrix A satisfies A2 − 4A + I = 0, then A is invertible and A−1 = 4I − A.…

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Q: The order of the single matrix obtained from 1 1 -1 To 1 23 is 1 0 21 -1 0 2 2 0 3 2 (a) 2 x 3

A: Here the order of the matrix needs to find out for both terms. Subtraction and addition won't affect…

Q: There is a unique value of h such that the matrix 2 3h/2] -1 3 1 h 4 0 h+1| is NOT invertible. Find…

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Q: If A and B are orthogonal nxn matrices, then AB-1 is an orthogonal matrix. True False

A: here we must know that  1)  AA-1=A-1A =I2) ATT=A3) AI =IA =A

Q: 13. a) Show that if A and B are n x n matrices, at least one of which is invertible, then AB and BA…

A: (a) If A and B are two n×n matrices, and one of them is invertible, then show that AB and BA are…

Q: 4 Is the matrix a linear combination of the ma- 3 and 1 ? Justify your answer. trices

A: A matrix A can be expresses as a linear combination of two matrices B and C, if and only if there…

Q: (6) Consider the real symmetric matrix (2 1 0 A = 1 1 2 Construct an orthogonal matrix Q of eigen…

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Q: (6) Consider the real symmetric matrix (2 1 0 A 1 1 1 1 2 Construct an orthogonal matrix Q of eigen…

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Q: 6 X1 -1 -5 X2 II

A: Let us consider the system of differential equation X'=AX then the solution of system of equation is…

Q: 29 What numbera in A-L makes A-QA@ possible (where Qis an orthognael matrix and A is an Zero or 1??

A: We shall solve this question by just using the definition of an orthogonal matrix. We know that a…

Q: 2. Find a single matrix equal to [1 - i 1+0, where i = √-1 (imaginary unit).

A: To find the product of the given 3 matrices.

Q: Determine the dimension 31 43 -8 21 Ab X of the matrix. AN

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Q: Let A be an n × n matrix.Suppose that the matrix B is obtained from A bymultiplying the jth row of A…

A: The matrix B is obtained from a n×n matrix A by multiplying the jth row of A by k≠0.

Q: A matrix of order m x 1 is called a Choose.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1) Find a diagonal matrix A that satisfies A-2 20,

A: Here, we need to find a diagonal matrix A such that A-2=2004