10. If a and b are two matrices, such that a. b=b.la, what is concluded? a = a a = a! a = a'

Q: Due to what property, applied to the matrices below, do we know that A + (−A) = O?

A: A+-A=O

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

A:

Q: If A and B are sk ew-symmetric 2 X 2 matrices, under what conditions is AB skew-symmetric?

A:

Q: 4- Determine the rank of the following matrices: [1 2 8] i- A = |4 7 3] [3 4 5] ii- A=|1 2 3 [4 5 6]…

A: i. Given: A=128476953  ……1

Q: 4. If det(Adj(A)) = then what is det (A-1) if A is a (4 × 4) matrix?

A:

Q: If an m x n matrix U has orthonormal columns, then UTU = I.

A:

Q: 2 3 uppose A = = B+C where B is symmetric and Cis skew-symmetric 5 6 b bi2 b12 b2 matrices, B = then…

A:

Q: How is the matrix of R^−1 obtained from that of R in general, that is, when A = {a1, . . . , am}, B…

A:

Q: Suppose A is a symmetric nxn matrix and B is any nxm matrix Show that B'AB, B'B, and BB' are…

A:

Q: 30 is similar-to 0. if and only if The matrix 03 O ant3 O b.a1 Ocaf0 O dat-1

A: We have to solve given matrix:

Q: 2) Suppose that A and B are nxn matrices that satisfy AB=AB. Show that AB = AB.

A:

Q: Show that these four matrices form a representation of the Vierergruppe, whose multi- plication…

A: 17.2.2 We have to show that given matrices  I,A,B and C form a Vierergruppe. Concept:…

Q: 4. Verify whether the two given matrices are similar. Justify your an- Swers Question a. 1 A = 1 and…

A:

Q: 7 Show that A = 13 and B = 4 2 are similar matrices by finding an invertible matrix P satisfying 2 A…

A: Given,A=7-132-4 abd B=1-2-22Let,P=abcd , and P=ad-bc=nSo, P-1=1nd-b-ca where n=ad-bc=dn-bn-cnan

Q: 6. If A is a 4 x 2 matrix and B is a 3 x 2 matrix, what is the size of ABT?

A:

Q: Suppose A and B are 3x3 matrices with det A = 2 and det B = -3. Find det(2BTA-B).

A:

Q: Suppose that A is a 4 x 4 matrix with det(A) = 5. Then + (24–1) - [2 Enter your answer exactly, as a…

A: We have to find determinant

Q: What is 'a', if B as shown below is a singular matrix?

A: A singular matrix is a matrix whose determinant is zero.

Q: 8.) If A is an mxn matrix, what are the largest possible value for its rank and the smallest…

A: As per the instruction, we will be answering only the first one. For (8), We have that A is an mxn…

Q: 4. Suppose that a matrix A can be writ

A: Given, a matrix A can be written as the matrix product A=BC as follows:…

Q: Compute the rank and nullity of the given matrices over the indicated Zp

A:

Q: Suppose Band C are n xn real matrices and A-B+jC is a Hemitian matrix then: 640 must be a…

A: I have prove C is skew symmetry matrix

Q: 4. Prove or Disprove: For anynxn matrix A, A A = AA.

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

Q: 6. Suppose that A is a 3 x 4 matrix. а. Is it possible that dim Nul(A) = 0? b. If dim Nul(A) = 1,…

A:

Q: If B arises from a matrix A by elementary row operations, what is the relationship between NS(A) and…

A: Given matrix B arises from a matrix A by elementary row operation. We have to find the relationship…

Q: Suppose the matrices P and Q have the same rows as I but in any order. They are "permutation…

A:

Q: What is the linear combination of the matrices аnd

A: The explanation are as follows

Q: (4) If A is a 3 × 8 matrix with rank 3, what are dimNulA, dimColA, and dimRow A? (5) If A is a 2019…

A:

Q: 4. Show whether that the following matrices are positive define, negative definite or neither A= 2.…

A:

Q: 8.) Find the LU-factorization of the following matrix 1 2 2 2 3. 1.

A:

Q: 7. If a n x n matrix B is obtained from A, using only m number of row interchanges, then det A det B…

A:

Q: 3- If A² [45] [95] 091 (1 find A where A is UPF triangula matrix

A:

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, B are 3 x 3 matrices such that det(AB 1) = 12 and det(adj(A)) = 16. Then det(3A". (B)1) %3D

A:

Q: 17 - Which of the equations given below on the multiplyability of the matrices shown with their…

A:

Q: 43 A and B are B,3 matrices where lAl = -3 and IBl =2. Giren this, what is |-2 AD-2|?

A:

Q: 4- Determine the rank of the following matrices: [1 2 8] [3 4 5] [3 9 2] iii- A = 1 5 6 l2 7 4] i- A…

A:

Q: Consider the following information regarding the number of men and women workers in three factories…

A: Represent in 3 x 2 Matrix form.

Q: 4. Verify whether the two given matrices are similar. Justify your an- Swers Question a. 1 1 3 and B…

A:

Q: 4- Determine the rank of the fcllov-ing matrices [1 2 8] 7 6 ii- A=|1 2 3 5 3. 13 4 3? i- A = |4…

A: for a 3*3 matrix if determinant is not equal to zero then rank is 3  if it is zero then we calculate…

Q: 8. If A is an mx n matrix, wh

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

Q: 6. Suppose A and B are 4 x 4 matrices where |A| = and |B| = 3, compute: (a) det (24)~!) (b) det…

A:

Q: and D be a diagonal matrix D = diag(A₁,..., An) such that

A:

Q: Consider a 2x2 matrices a  b c  d a,b,c,d are subsets of {1,2,3}. If you were to form a matrix at…

A: Each of a,b,c,d has 3 choices. So there are 34=81 possible matrices.A matrix will not have inverse…

Q: If Ā is a 5 × 5 skew symmetric matrix, show that det Ā = 0.

A: A n×n order matrix A= is said to be skew symmetric matrix if the following condition hold…