If UT = U-1, then matrix U is an orthogonal matrix. %3D O True O False

Q: If the RREF of A|I is I| B, then AB is the identity matrix. A True B False

A: We have to check whether the given statement is true or false.

Q: For matrix A, B if A – B = O, where O is a null matrix then * A = B B = 0 A = 0

A:

Q: If a square matrix A is not invertible, then the columns of A could be either linearly independent…

A: We know that if a matrix is invertible then its column are linearly independent. Column A is…

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: Find an LUfactorization of the given matrix.

A: Given, To find LU factorization of the given matrix.

Q: If the matrix A is positive symmetric definite, is BTAB also positive symmetric definite?

A: Let us define the function as, A¯=BTAB Then, A¯T=BTABT=BATBT=BABT   [A is symmetric]

Q: Suppose that A is an m x n matrix and B is an n x m matrix. Then the equation (AB) = ATBT is always…

A: Multiplication Property of transpose : We know that the transpose of a produce of two matrices will…

Q: A symmetric matrix A is positive def

A:

Q: If A can be row reduced to the identity matrix, then A is not invertible. True False

A:

Q: If A is a square matrix, then Ker(A) = Ker(RREF). True or false?

A: If A is aquare matrix then we have to check Ker(A) =Ker(RREF(A))

Q: If A is a nonzero matrix of the form P, then Rank(A) = 2. а

A: Let A be a n×n matrix . If Determinant of A is not ZERO, Then   Rank(A)=n

Q: Is it possible for a matrix to be both upper triangular and lower triangular? Oa. Yes O b. No

A: Solution

Q: Matrix A: 1 3 4 6.

A:

Q: If A 0 is a square matrix, then A is invertible.

A: Given: Any square matrix A≠0 Assertion: If A≠0 is a square matrix, then A is invertible. To prove:…

Q: A matrix A is similar to matrix B, if for some invertible matrix P, B = P''AP. Is B similar to A?

A:

Q: If A is a skew-symmetric matrix of order 5 then adj(adj(A5«5)) = %3D

A:

Q: If the columns of a matrix A are linearly independent, then dim Null(A) = 0. True False

A:

Q: If A and B are square matrices of the same order, then (AB)T = AT BT True False

A:

Q: If A is a square matrix whose diagonal entries are all zero, then detA = 0.

A: Given information: A is a square matrix whose diagonal entries are all zero.

Q: Is the following matrix 'B' diagonalizable?

A:

Q: If A is a skew symmetric matrix, what type of matrix is A T ? Justify your answer.

A: Given: A is a skew-symmetric matrix.

Q: Let A = diagonalizable matrix( A = XDX-1), then X and D are: LO H O4

A:

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

A: GivenA=3121

Q: b) If C is an orthogonal matrix and D = C + C-1 show that D is a symmetric matrix.

A: We have to show D is symmetric.

Q: If A is a square matrix such that A =1, then A'is equal

A: Given, A is a square matrix such that A2=I.

Q: If A is a square Matrix such that A'-A, what are the possible values of det A?

A: Determinant possible values

Q: The matrix A = is an orthogonal matrix. True O False

A:

Q: If A and B are n x n matrices, and vector v is in the image of both A and B, then i must be in the…

A: True or false.

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: is an orthogonal matrix? Determine whether or not gonal. Justify your response. -1 2 V3 V10 V15 2.

A: INTRODUCTION: If a square matrix Q is an orthogonal matrix, then it must have the property QTQ=QQT=I…

Q: Identify a matrix P that diagonalizes 2 6 A = a. 1 P = - 2 Ob. P = -1 0 0 2 Oc. P = 01 1 2 O d. -2 P…

A: Solution

Q: 4. A matrix A is similar to matrix B, if for some invertible matrix P, B = P'AP. Is B similar to A?

A:

Q: If A is an mxn matrix then rank(A) 2 min(m, n) Select one: O True O False

A:

Q: If A is an m x p matrix and B is a p x n matrix, then their product AB will be?

A: Two matrix can only be miltiplied if number of column of first matrix is equal to number of row of…

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: If A is a skew symmetric matrix, what type of matrix is AT ? Justify your answer.

A: If A is a skew symmetric matrix, then our aim is to tell the type of AT matrix?

Q: If a square matrix A is similar to the n x n identity matrix, then A = I, O True O False

A: We will use the definition of similar matrix to give the right answer of the question

Q: If 4 [a] is a 3x3 matrix, such that ay i (2m-j) then the diagonal elements are

A:

Q: An n x n matrix A is invertible if and only if it is row equivalent to I. O True False

A: Given statement is "An n×n matrix A is invertible if and only if it is row equivalent to In."

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

A:

Q: a) If A is a 5 x 5 skew symmetric matrix such that 5A + BT – 315 = 5(B – A)", 5 then |B| = ()".

A:

Q: Enter a 3 x 3 symmetric matrix A that has entries a11 = 1, a22 = 5, a33 = 4, a12 = 3, a13 = 2, and =…

A: Given A is 3×3 Symmetric matrix with entries a11=1 , a22=5 , a33=4 , a12=3a13=2 and a32=0.We know…

Q: Suppose A is a 10x10 invertible matrix. Then A is row equivalent to the 10x10 identity matrix. A)…

A:

Q: If A is a skew-symmetric matrix of order 5 then adj(adj(A5x5)) =

A:

Q: If the RREF of A|I is I | B, then AB is the identity matrix. (A) True B) False

A: We are given the RREF of A|I is I|B, we have to find whether AB is identity matrix or not

Q: If U is a square matrix such that UTU I, what can we say about det (U)?

A:

Q: Let A be a 3x3 matrix where A2=I3, then det(A) is 1 or -1. Select one: 1-True 2-False

A: To find- Let A be a 3×3 matrix where A2 = I3, then detA is 1 or -1. True False

Q: [5 Let B =E dl: Is the matrix B orthogonally diagonalizable? If yes, find a diagonal matrix 2 0…

A:

Q: If A is a 2 x 2 skew symmetric matrix, must det(A) = 0?

A: we have a 2×2 skew symmetric matrix.