Are there values of r and s for which [ 1 0 r- 2 0 s- 4 r+2 | 3 has rank 1 or 2? If so, find those values. The matrix has rank for r= i S = i O N

Q: which of the following are true? If A has dimensions m×n and B has dimensions n×r, then AB has…

A: If A has dimensions m×n and B has dimensions n×r, then AB has dimensions m×r. This statement is…

Q: Let [1 2 [1 A = 2 41 1 3 and B = |2 1 [2 2 6] 2 4] 3 [1 2] Find the elementary matrix, E such that…

A: Two matrices A=124213102 and B=124213226 are given. We have to calculate the matrix E that satisfies…

Q: Find the elementary matrix E such that EC A where [2 4. 2 -1 2. -2 and C = 4 A 2 -1 -2 8 -6 [16 10 E…

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Q: If A and B are two n x n invertible matrices, then one of the following is always correct a) (AB)T =…

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Q: Let A be a 5 x 9 matrix. Which of the following statements is (are) true? Ob and d O c) Nullity of A…

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Q: If A and B are similar, then there exists a matrix P such that B = PAP. Use this fact to fi -2 2 -3…

A: Here we have to find B5 ,   We have to find if A and B are similar or not, if A and B are similar…

Q: 2. Find the values of x such that the rank of matrix 3x – 8 3 3 3 За — 8 3 - 3 3 3x – 8 is less than…

A: See the attachment

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: [1 2 0] 3. If is A =3 4 0 create a matrix B whose entries are three times the difference of an…

A: Since I have solved similar ones, Let us find the matrix B and and it's determinant using built in…

Q: Given that P and O are 3 x 3 invertible matrices then (A-"B) = A. AB-! B. B-'A C. B-'A-! D. BA-

A: Given : A-1B-1

Q: Let A be an 8 x 8 matrix with det (A) = -2. Let B be the matrix that can be obtained by applying the…

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Q: Given the matrix 0 -5 11 6 Introduce the "- R" term to the diagonal of the matrix. -5 - R (A 11 - R…

A: Given query is to add -R in diagonal of matrix.

Q: For the matrices 2 4 0 -2 and B = 1 A = -3 1 in M, 2, determine whether the given matrix is a linear…

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Q: A is a 3 x 3 matrix, det(A) = -2. What is the value of det(3A)? %3D -6 O 54 O -54 O 6 O 27

A: Given :-  A is a 3×3 matrix , det A =-2. To Determine :-  The value of det 3A.

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: Give the value(s) of a for which the columns in the matrix 9 6 -6+a A= 6 12 -6 -6+a -6 are linearly…

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Q: The value of x for which the matrix A = (, ) is singular is a. 0 b. 6 c. -6 d. 12

A: The correct option is C .i.e. -6 .

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: If A and B are 5 × 5 matrices such that AB = –BA, then AB is singular. If (AB)² = A²B², then AB = If…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: For the matrix A. det(A) = 16 B. det(A) = -30 C. det(A) = 0 O D. det(A) = 30 OE. det(A) = -16 %3D

A: We try to solve determinant using some elementary row operations.

Q: - E- is multiplied by is equal to zero, then matrix If matrix A 3 B1 C.o D-2

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Q: 6. The trace of the n x n matrix A, denoted Tr A, is the sum of the entries on the main diagonal: Tr…

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Q: If A and B are similar, then there exists a matrix P such that B* = P A*P. Use this fact to find B",…

A: i have just used the information given there in your example

Q: If A and B are two n x n invertible matrices, then one of the following is always correct a) (AB)" =…

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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: Let A and B be nx n matrices. Which of the following statements are always true? (i) (AB)² = 4²B?

A: i   AB2=A2B2-Not Trueii   Ax=0 has infinity many solution then A is not inversible .…

Q: 7. Find values for x and y that will make the matrices equal. X = y = T AM H. 1 x+y 3+x 3. 4 -2 5y…

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Q: 4 Given matrix A = : 1, find x such that -2 the matrix is singular. а. О с. 3 b. 2 d. 6

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Q: Consider A 3 Then what is the matrix S that transfer A to a diagonal matrix D. [2 and D and D = S =…

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Q: Let A, B, C be n x n matrices. Show that if A is similar to B and B is similar to C, then A is…

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Q: If A is a 2x2 matrix such that trace(A) = det(A) = 3, then what is the %3D value of trace of (A-!) ?…

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Q: 3. Let A, B,C be n xn matrices. (a) Show that rank(AB) = rank(B) if and only if the systems (AB)x 0…

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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 the two matrices similar? If so, find a matrix P such that B = p-1AP. (If not possible 1 0 0 1 0…

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Q: Let A be a 7x6 matrix such that Ax O has only the trivial solution. What is the rank of A? O A. 6 О…

A: Use the given information.

Q: If A is a 4x6 matrix and T is a linear trạnsformation such that T: x Ax, then Select one: O a. The…

A: Topic- Linear  Algebra

Q: If the product M = ABC of three square matrices is invertible, then B is invertible. (So are A and…

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Q: If A = and P = then the similar matrix of A is: 0.5i A) 15 -0.5il B) , [-1.8i D) -0.4 1.4 0.8il 2.5…

A: It is given that the matrix is A=2i01-2i. To find the similar matrix of A. Note that: A matrix A is…

Q: Which of the matrices below are elementary? For those that are, describe the corresponding…

A: Since you have posted multiple sub parts, as per our policy we will answer first three sub parts.…

Q: -1 Find the matrix P that diagonalizes A = -2 and the resulting diagonal matrix D. 3 -1 D = P = Ex:…

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Q: 3. Let A, B,C be n xn matrices. (a) Show that rank(AB) = rank(B) if and only if the systems (AB)x=0…

A: (a) Let rank(AB)=rank(B). Hence by rank-nullity theorem,  null(AB)=null(B). Hence every solution of…

Q: If B is invertible matrix, then (4BT) -1 (A) 블B-1 (B) 4 (B-1)" (C) 4 (B")¯1 (D) 를 (B-1)" (E) BT

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Q: If det (A) = 0, then two of the columns of A are the same, where A is an n × n matrix. True

A: False

Q: 12. Let A be a 3×3 matrix, and suppose that the matrix B is obtained from A by the following row…

A: Remark: Effect of elementary row operation on a matrix: If two rows of a matrix are interchanged,…

Q: The values of x, y, and z that makes the matrix 1 x - 2 -1 x + y %3D -3 -1 symmetric are O None of…

A: A symmetric matrix is a square matrix that is equal to its transpose.

Q: a b A = | d f e k compute Aē1, Ae2, and Aē3. (b. If B is an n × 3 matrix with columns ī1, v2, and…

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Q: 7. Let A, B and X be square matrices of the same size. Using the algebraic properties of matrices to…

A: See the detailed solution below with rules.

Q: Give the value(s) of a for which the columns in the matrix 8. -4 4 A = -4 +а 5 -6 4 -6 10 + a are…

A: We will find out the required values.