D If A is a square matrix and B= A". (A - A"). A show that matrix B is an inverse symmetric matrix.

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 is an 7 x 12 matrix, then what is rank A² + dim nul (A²) equal to? Your

A: We can solve this as follows:

Q: Enter a 3 x 3 symmetric matrix A that has entries a11 = 0, a2 = 2, a33 = 5, a21 = 3, a31 = 4, and…

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

Q: For which values of the constants b and c is the follow- ing matrix invertible? 1 b -1 -b

A: The given matrix is 01b-10c-b-c0

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: If A is an m xn matrix, then A and AA have the same rank. O True O False

A: Consider the statement  If A is an m×n matrix  then A and ATA have the same rank

Q: If A is any matrix, to what is tr (AA T) equal?

A: Let A=[aij] be n X n matrix. Then  AT=[a'ij] where a'ij=aji Let C=AAT=[cij] , where

Q: The inverse of a matrix A is written as A- such that AA-1 =A-A=

A: Clearly we know that, AA-1 = I.

Q: Let A be an m × n matrix. Show that A is row equivalent to O if and only if A = O .

A: Consider the given information as A be an n×nmatrix

Q: Suppose that Q is an orthogonal matrix, then O a lQ°| = 4 O b. Q°| = 2 O d. Q°| = 0

A: This question is related to Linear Algebra

Q: Given matrix A, A + −A = _____?

A: To Determine: find A+-A Given: we have a matrix A Explanation: let us consider a matrix A=1245 then…

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: If A is an m x n matrix then A' A and A have the same rank. true false

A:

Q: Let A be an n xn matrix andB=A+1, where / is the identity matrix, then it is possible for A and B to…

A: False

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: Which of the following is the LU-factorization of the matrix a) 1 b) 0 1 1 c) d)

A:

Q: Show that A = 3 and B = are similar matrices by finding an invertible matrix P satisfying A = P-'BP.…

A: We are given two matrices A and B and we have to show that these are similar matrices.For this we…

Q: For a square matrix A, AAT = AT A. A True В False

A:

Q: If A is a 5 x 5 matrix then l-A| = |A| |A| O True O False

A:

Q: Find a matrix A to safisty the following equation: -1 (AT – 5 2 3 1

A: to find the inverse of 2*2 matrix, the formula is

Q: 2 if A=| -3 -2 4 and B= 1 ,find the Matrix X such that 3A+4X=5B 1 3

A:

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 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: 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: A matrix A is similar to matrix B, if for some invertible matrix P, B = P''AP. Prove that if A is…

A:

Q: Let A be a 3 x 10 matrix, and let B be m x n. Suppose that B'A' is a 21 x 3 matrix. What is the…

A:

Q: If A is square matrix of order 3 such that|3 A| = 54. Find |A|

A: Using the properties of determinants

Q: Let A be a square matrix and det(A) = 2. If B is the matrix that results when –7 times the - first…

A: Given that: det(A)=2

Q: Find a 3 × 2 matrix T, such that TT' = A, where 4 A = |4 3 3 5

A: Given: To find a 3 x 2 matrix T, such that TT' = A,  A = 540453035

Q: 4. If A is a nonsingular nxn matrix, show that AA¹ is nonsingular and det(AA) > 0.

A: Given A is a nonsingular matrix.

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

A:

Q: Given a matrix A = for what conditions on a, b, c, and d will the matrix not have an inverse?

A:

Q: Find matrix A, given that: :) 8. -2 2A-1 10 9.

A: NOTE: Refresh your page if you can't see any equations. . divide both sides by 2 take inverse on…

Q: If AT = A-1, where A is a real matrix, then A is

A: When transpose of A equal inverse of A , then A is

Q: esponse. stion 10 If A is an mxm triangular matrix, then det(A) equals the product of the diagonal…

A: Introduction: A square matrix has a determinant. It is a scalar quantity. The determinant has a very…

Q: Consider the matrix A = Calculate a22 = 8 5 d n -( :-(29 766 b f 468 h с Calculate 932 = a e

A: It is provided that: A=852766468·dngbfahce. We need to calculate a22, a32.

Q: If A is a 5 x 5 matrix then -A |A| True O False

A:

Q: If A is a square matrix such that A3 = O, show that (I-A)~l = I + A + A2.

A: To prove that (I-A)~l = I + A + A2 If A is a square matrix such that A3 = O

Q: Let A and B square matrices where detA=4 and detB=12. What is det(A-1B)?

A:

Q: If A and B are nXn matrices, then (AB)²=A²B? A True

A:

Q: If A is a square matrix, then A2 is defined. TRUE OR FALSE

A: For matrix multiplication to be defined, the number of columns in the first matrix must be equal to…

Q: Find Hhe uinuerse of the matrix (if it exis ts). (if an answer does not exist, enter DNE.) 1 -3 -1…

A: Note:-  We’ll answer the first question since we answer only one question at a time. Please submit a…

Q: If a and b are the matrices of order 3 and (A)=5,(b)=3 then find the vailue of 3ab?

A:

Q: Let A be an n xn matrix and B= A+1, where I is the identity matrix, then it is possible for A and B…

A:

Q: Suppose A is a 5 by 5 matrix with det(A) = 6 What is det(AT A)? Answer:

A: Given det(A) = 6

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

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

Q: Show that A is similar to B by showing that A and B are similar to the same diagonal matrix, where…

A: