Thich of the following is a non-singular matrix P such that PAP is diagonal if 7 0 ? -4 2 A =

Q: 3. Let A = 1. ). Compute eat in two different ways: (a) by exponentiating the equivalent diagonal…

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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: Find the elementary matrix E such that EB = A where %3D 2 3 1 2 3 1 A = 4 -3 -2 and B = -8 6 4 7 -6…

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Q: Find the elementary matrix E such that EB = A where %3D 5 4 1 ] 4 1 A = |4 |7 -6 1 -1 and B = |12 3…

A: EB=A multiplying with B-1 on both sidesEBB-1=AB-1E=AB-1

Q: A is a square matrix that's n x n. A21=0 a) In-A is invertible, show why. b) B is invertible. Is B-A…

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Q: 12 Let A be a square non-invertible matrix. Which of the following is not true? Select one…

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Q: Find the elementary matrix E such that EB = A where 3 1 2 3 1 A = |2 -1 -1 and B = |4 -2 -2 7 -8 4 7…

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Q: In the given question find an elementary matrix E such that B=EA.

A: given,       A=21-13  ,  B=-1321

Q: An n x n matrix A is orthogonal if AA" = I. If A is orthogonal show that det(A) = ±1.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Some of the entries of the 3 x 3 matrix A are known as A -1 1 If det (A) = -–6 and A-1 find x.

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Q: (4) Let A E R™xn be any matrix. Solve the following problem min ||AX – I||r Hint: Write X = [x1,...,…

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Q: In cach of the following, write the matrix A as a product SDS, where D is a diagonal matrix. ( ) 10…

A: We have to diagnose the above matrix.

Q: Find the elementary matrix E such that EB = A where 4 1 4 4 1 3 -1 -2 and B 18 -6 -12 %3D 5 -7 4 -7…

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Q: 0. is similar-to e matrix if and only if 0 3 03

A: A and B are similar matrix if there exist an invertible matrix P such that  B= PAP-1

Q: -4 -4 4 M = 12 15 -14 -35 + k -27 26

A: The given matrix is  M=-4-441215-14-35+k-2726 If the determinant of the matrix is zero then the…

Q: 2. (a) Suppose (B − C)D = 0, where B and C are m x n matrices and D is invertible. Show that B = C.…

A: Explanation of the answer is as follows

Q: Which of the following is both symmetric and skew-symmetric? O None of the these. A matrix cannot be…

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Q: D M 2P] 3 3. If A =| K [-P R s is a singular matrix then find the value of P.

A: Given a matrix, A=DM2PK3S-PRL. Let, D=1, L=9, P=f, S=1, N=8, K=9, M=3, R=5. Then, A=132f931-f59  To…

Q: If G = X| is alx1 matrix, and A is a 1xn matrix, is it true that XA = GA for an)- any number A. Is…

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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: Find the elementary matrix E such that EB = A where 4 1 2 4 6. 1 A = 2 -3 -1 and B = -4 2 6 -8 -8 2…

A: To find E such that EB = A

Q: Suppose that A and B are invertible n x n matrices. Which of the following statements is true. A.…

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Q: **32. Suppose A is an m x n matrix and x e R" satisfies (ATA)x = 0. Prove that Ax = 0. (Hint: What…

A: Here we use property of modular and dot product.

Q: Show that if An = O for some positive integer n (i.e., if A is a nilpotent matrix), then det(A) = 0.

A: We have An=0. So xn is an annihilating polynomial of the matrix. So the minimal polynomial is xm for…

Q: Let A be a square invertible matrix. Which of the following is not true? Select one alternative: O A…

A: Since given A is invertible matrix, so det(A) is not equal to zero. It is always true. we also know…

Q: Find the value of k so that matrix A singular. 1 1 1 -k A = 3 2 -6 -2 2k O 1 3 O None of the above

A: topic- matrices and determinant

Q: I find the cooridinate matrix for A realtive to S=SA, Ag „Az, Au? where A= [2 0 and 1 1 00

A: The coordinates matrix for A is [a b c d]=aA1+bA2+cA3+dA4=A .see 2nd step.

Q: 7. The rank of an identity matrix of order n is: А. п - 1 В. п C. n+1 D. 0

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Q: (a) The matrix ( (AB)-1 )T comes from (A-1 )T and (B-1 )T In what order?(b) If U is upper triangular…

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Q: ?) A is an n x n matrix, such that 2A3 – 4A? + 6A – 21 = 0 (where I is the identity matrix and 0 is…

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Q: Let A and C be n×n matrices such that ​CA=I​ (the n×n identity​ matrix). Show that Ax​=0 has only…

A: Here, CA=I, where I is the identity matrix.

Q: Give the value(s) of à for which the matrix A will be singular. -4 1 -2 A= 0 1 A 2 A={-2, 1} b)…

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Q: For a matrix A having JA| = 0, which of the following are true? * O A- exists with |A¬' |= 0| O A-…

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Q: A is akxl matrix with rank r and nullity n. If 2r + n = 10 which of the following cannot be the…

A: it is an application of rank nullity theorem.

Q: Find all the values of k for which the following matrix will be singular. 1 1 -1 0 k -2 k 3

A: A matrix is said to be singular if its determinant is 0.

Q: Find the elementary matrix E such that EB = A where 4 4 1 4 4 1 A = |4 -3 -2 and B = | 20 -15 -10 7…

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Q: What is the det(A) if a matrix has p(A)=13 - 212 -A +3 as its characteristic polynomial. O A. -2 В.…

A: Proceed as shown below...

Q: Find the elementary matrix E such that EC = A where 3 3 -2 1 3 3 1 A 4 -1 and C 4 -2 -1 -6 3 20 9. 8…

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Q: Which of the following is an elementary matrix? 1 0 1 В. 1 C. 0 0 1 A. 5 1

A: Given : Matrices A.  10-51 B. -5110 C. 110001000 D. 2002010000100001   To find : Which of the…

Q: •(b) A = B:

A: Given,        A=-1201,   B=1-201

Q: Which of the following must be true? For any two n x nmatrices A and B, we must have AB = BA For an…

A: M3+M2=2M is correct.

Q: If A and B are singular n × n matrices, then A + Bis also singular.

A: If A and B are singular  matrices the A+B is also singular. (False Statements)

Q: If A? is a zero matrix, then AT A = 0 is: %3D O a. Not possible unless A is a zero matrix O b. not…

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Q: 10. Assuming that all matrices are n x n and invertible. Solve for A (CDF ACB-C = D¯ B-'C EP Type…

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Q: Find the elementary matrix E such that EC = A where 3 3 -3 1 3 3 1 A = -1 and C = 2 -3 | 8 -7 2 23…

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Q: 4. Find a diagonal matrix A that satisfies the given condition. 16 At = 0 81 0 1. 01

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Q: 2 Suppose A = is positive semi definite matrix then: 10 O a. a < -V20 O b. a = ±v20 O c. lal < 20 O…

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Q: Find k for which the matrix below is NOT invertible. 1 1 3 -1 2 1 k

A: For matrix to be non-invertible, it's determinant must be 0. We will use this property to find the…

Q: q4: If  det(A) =|A|= 0, then A is called a non-singular matrix  True  False

A: Non-Singular matrix: A non-singular matrix is a square matrix whose determinant is not equal to zero…

Q: [*:* а + 2 а (10) Find all a E R for which the matrix is singular. 1 а

A: Remark: A square matrix A of n is said to be singular if and only if det(A) = 0. i.e., Its…