-2 A = C = (1) Find a matrix B such that AB = C. B = (2) Find a matrix D such that DA = C. D =

Q: I. State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c)…

A: a) A matrix is upper triangular if all the elements below the main diagonal is zero Hence it is not…

Q: -1 Give the co-factor of matrix C, where C = 1 2 1 1 5 2 1 1 -1 2 -4 5 2, -1 3 1 B -2 6. -2 3 -9 3…

A: Given,            C = 1-1-4125112

Q: • The Matrix B from 3 x 2 at by = 1- is 1. 3. 4. 1 -2

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Q: Let A be 2 x 2 matrix, if the matrix B results from A by adding 3 times the first row of A to the…

A: The objective is to find out the correct option.

Q: A? 0 0 A =

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Q: Find the characteristic equation of the matrix: 4 C = 2 -2 2.

A: Characteristic equation of the matrix C is given by  det ( C - λI ) = 0

Q: Let A be a 5×5 matrix such that Ax​=b has a solution for every b in R5. Is it possible for Ax​=0 to…

A: Here, Ax=b has a solution for every b in R5

Q: Let A be a 3 x 3 matrix such that A3 - 6A² + 4A – 31, = 0. Then, A is invertible and A

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Q: -x-1 -x 2 Let A = 1 2 (i) Determine an expression for det(A). (ii) For what values of x will the…

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Q: 9. Solve the matrix equation C-A(X - B) = D for X. Note that A, B,C, D, and X are all n x n…

A: Explanation of the answer is as follows

Q: 2. (a) Express -2+t+t +r' as a linear combination of 1-t, 1+r, and 1+1- or show that it cannot be…

A: We have to write in the linear combination.

Q: Let A 1B = 5 l, and C-1 = If X is a matrix that satisfies: %3D %3D 2B = Al2 - XC then X is

A:

Q: 3- -4 0 1 2 1 - Find the adjoint matrix adj(A). 0 -1 Let A = 3 1 -2 3 -1 -1 2 a) 1 b) -1 2 1 2 -1 0…

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Q: Consider the matrix 3 2 - А — 1 2 1 5 2 - 1 | Use Gaussian Elimination to find the inverse of the…

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Q: Find 2 X 2 matrices A 0 and B # 0 such that AB = 0. Can you find a matrix A + 0 such that A2 = 0?

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Q: A matrix A is similar to matrix B, if f invertible matrix P, B = P'AP. Prove is similar to B and B…

A: Given that: A is similar to B such that: B=P-1.AP.

Q: Which of the following matrices is a nilpotent matrix of degree 2. a a) where ab =-x². -x a where ab…

A: We have to select the nilpotent matrices of order 2 from the above list.

Q: 2 3. Let A be an invertible matrix such that A-¹ = 0 1 2 1 3 0 1 01 Solve the system (2A²)x= b,…

A: Given is the matrix A-1=220011-130,b=4-13 The objective is to solve the system (2A2)x=b.     Any…

Q: 9. Solve the matrix equation C-A(X B) = D for X. Note that A, B, C, D, and X are all n x n…

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Q: Prove that the quadratic equation A^2 - 3A = 2I hold true for the matrix A =  5  -6  -6        -1…

A: The detailed solution is as follows below:

Q: Find the SVD of the matrix: 1 2 34 A = 0 0 0 0

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Q: Find all a,ß>0 so that the matrix 3 2 B [4]= a 5 B 2 1 a is strictly diagonally dominant.

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Q: 2 In what direction does f(x) = 7xy - 9x increase most rapidly at (4, - 1)? V f(4, - 1) = (Type an…

A: I am attaching image so that you understand each and every step.

Q: -42 -36 Let A= and let B = 33 15 Solve the matrix equation for X : 3X = 3A – B. %3D

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Q: Let A be the matrix a- [}] 3 1 A = Which answer is correct for the A ?

A: GivenA=3121

Q: a) ir(A - 1)1- ( -2) %3D Find the matrix A

A:

Q: (b) Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 3 -21…

A: Given;                           A=13-223001-1 Start with A I…

Q: Let A, B, and C be invertible matrices. Then (4A-1B"C²)-1 is equal to c--(B")-1A equal to the above…

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Q: -4 Find the change-of-coordinates matrix from B to C. - 10 Let B- (b, (b.b2) and C- (c,,©2} be bases…

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Q: -1.T If A is 3x3 nonsingular matrix such that AA' =A'A and B=A A' then BB' = Select one: (B*," b. в…

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Q: -1 1 Verify that the matrix A = 3 is diagonalizable; 4 -2 5

A: We will use condition for matrix to be diagonalizable

Q: Suppose A-A, where A is the matrix. The det (A) is

A: Determinant of a null matrix is equal to zero.

Q: A lower triangular matrix of matrix A is c. L = Ex Ek1... E, E,. ... Ek1 E, d. L = E, E, a. L = E,…

A: A lower triangular matrix of matrix A is  .......

Q: 3 b Find the value of b that make the matrix A singular. 3 5 b =

A: Note : According To our guidelines we can solve only first question and rest can be reposted.Thank…

Q: If A is invertible matrix, then (2AT) %3D (A) 를 (4-1)" (B) 2 (A-1)" (C) 2 (A")-1 (D) 글A-1 (E) AT

A:

Q: 2] find 1 -1 3 - If A = and B 1 |3| -2 (а) ЗА — В. - (b) The matrix X such that 3A – B+ 3X = 0. ||…

A: As per guideline we have to solve only three parts

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: 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: Are there values of r and s for which 1 0 r- 4 4 0 s- 2 r + 4 5 has rank 1 or 2? If so, find those…

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Q: 3. Let A be an invertible matrix such that A-¹ = NOT 2 0 1 2 01 1 1 Solve the system (2A2)x= b,…

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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: '-2 -1] [3 5 B= 0 T-1 2 0 | 2 0 3 4. Let A, B and C be the matrices A= 1 and C = 3 Find a matrix X…

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Q: a For what values of a, b, and c is the matrix -a invertible?

A: For no values of a, b, c the given matrix is invertible.

Q: Suppose that A is an n × n matrix satisfying the equation A4 + 2A2 − 3A − I = O , where I is the…

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Q: 1. Identify the two-by-two matrix with matrix elements a;j = i – j. O (1 (금) ㅇ(9) (오 ㅇ (? )

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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