Let A be a 3 x 3 matrix such that det(A) = 2. Evaluate det(Aª) and det(2A).

Q: Find x such that the matrix is singular. 4 A = -2 -6

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Q: Let A be an 3 x 4 matrix. What must c and d be if we define the linear transfor- mation T: R → Rd by…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: Let A = - 2     1    0                 1     0    1                2    -3    1        A is a…

A: trace is the sum of all diagonal elements of the matrix.

Q: let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C0 or A=0

A: WE have to check the meaning of cA=0.

Q: Let A = a be an invertible matrix. Then a formula for the inverse A-1 is given by d]

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Q: Let a be a real number, and consider the matrix a 2 1 1 6 3 A =

A: Given:

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists)

A: Given matrix is,

Q: Use the Cramer's rules to solve the matrix equation A. X = B, where 1 0 1 1 1 0 1 -1 0 -1 A = B || 1…

A: We have to solve the matrix equation A.X=B, where A=101101-1011000101,B=1-121

Q: Find x and y such that the rank of matrix A is 2. 1 0 a – 1 0 у- 2 г+1 -5 A = 4 x = Ex: 5 Ex: 5 С y…

A: We are using rank nullity theoram  Rank(A) + nulity(A) = number of coloumn in A.

Q: For the matrix A , use the Cayley­Hamilton Theorem to compute A -1 and A -2 by expressing each as a…

A: According to Cayley Hamilton theorem, any square matrix satisfies its own characteristics.

Q: Find all pairs (x,y) for which matrix B is not invertible, where 1 1 B = 2 1 1 0 -1 y

A: Here we will apply the condition for a matrix not being invertible to solve this question that is…

Q: Find x such that the matrix A is nonsingular.

A: Given: The inverse of a matrix is given as follows,

Q: 3. Find x such that the matrix A is equal to its own inverse. A = G %3D

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Q: Let A be a matrix 4 0 0 0 0 4 0 0 0 0 2 0 1 0 0 2 Determine if A is diagonalizable, and if…

A: Solving the above matrix problem using row operations

Q: Suppose A is a 2 x 2 matrix such that A and 1 A What is A-1?

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Q: Let A be an n xn matrix and B= A+ I, where I is the identity matrix, then it is possible for A and B…

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Q: For this matrix A, find a diagonal matrix D and invertible matrix P with inverse P such that A = P D…

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Q: Find x such that the matrix is singular. A- -2

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

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Q: If A is an invertible n X n matrix, show that adj A is also invertible

A: Given: To Prove: Concept: 1. 2.

Q: Show that ∣A∣ = ∣AT∣ for the matrix below.

A: Now the transpose is,

Q: Find the inserve if it exists, of the following matrix. 1 -1 2 1 1 1 1 2

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Q: Find a 3 × 2 matrix T, such that TT' = A, where 4 A = |4 3 3 5

A: Given: To find a 3 x 2 matrix T, such that TT' = A,  A = 540453035

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists).

A: To: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists). a001a001a

Q: If A is a 2×2 matrix such that trace(A) = det(A) = 3, then %3D value of trace of (A-!) ?

A: Introduction: It is the sum of the diagonal elements of the matrix from upper left to lower right.…

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 1 -1 A =0…

A: Given,

Q: Find conditions on w, x, y, and z such that AB = BA for the matrices below.

A: Here we find the condition w,x,y,z such that AB=BA where A=wxyz , B=11-11

Q: Let A be a 2 x 2 matrix. If det (A) # 0, then det (adj A) = det (A).

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Q: Let A be 3 x3 R given matrix by over 2. A = -1 Using the result of A find the value (s) of makes the…

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Q: Given A = [010; 0 0 1; 0 0 0], B= [0; 0; 1J, Calculate the rank of the Controllability matrix

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Q: Use the Cayley-Hamilton theorem to find A1, A°, and A“ for the given matrix A. 1 5 1 A = 0 2 1 0 0 2

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Q: Let B = and B' = Find the change of base matrix from B' to B and from B to B'

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Q: Find x such that the matrix is singular.

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Q: 4 3 A = 1 2 2 4 1

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Q: For the matrix A, find an orthogonal matrix P such that P-'APis diagonal. 3 00 A =| 0 2 2 0 2 5

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Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 6 -2 -4…

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Q: Let A be a 6 × 5 matrix. What must a and b be in order to define T : R“ → Rº by T(x) = Ax? Ах?

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Q: Let A be the matrix Find p(A). p(x) = x' - 2r + 4

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Q: Find all a > 0 and B>0 so that the matrix 3 2 B A A =| a 5 B 1 is strictly diagonally dominant.

A: The given matrix,A=32βα5β21α

Q: Find the value of k such that matrix A is singular: (1 2 A = | 5 -1 2 6. k.

A: Singular Matrix: A square matrix that is not invertible is called singular or degenerate i.e., it is…

Q: snip

A: If a square matrix A of order n is invertible then |A|≠0

Q: Let A = (a;;)ij be an m x n matrix of real numbers, and let f : R" Rm be defined by 0-0 x2 x2 f = A

A: To find the derivative of f given: matrix A which has m rows and n columns  also the function f…

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: Find x such that the matrix is singular. x 5 A = -3 2

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Q: (b) Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, [1 3.…

A: Given :          A = 13-223001-1   To find the inverse of A. Also, to compute 3A-1.

Q: Let A be a 3 x 3 matrix such that det(A) = 12. Suppose B is obtained from A by applying the…

A: We have to find the  det(B).

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists)

A: Given a matrix, Let A=0111 over Z2 To find the inverse of A.

Q: a Let A = b be 2 x 2 matrix such that d 3A' +2 Find A. 1

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Q: Let A be a 6 x 5 matrix. What must a and b be in order to define T : Rª → R* by T(x) = Ax? II

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