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

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

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Q: Find x such that the matrix is singular. 4 A = -2 -6

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Q: 2. Show that if A is an n x n real symmetric matrix then (Ax) y = x (Ay) for all x, y E R".

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Q: Does there exist an 8 x 8 matrix A - (a) satisfying the following three conditions? (1) If i 2j then…

A:

Q: Show that if A is an upper triangular matrix, then A T is lower triangular.

A: A is an upper triangular matrix. That is, Now let A=aij be a n×n upper triangular matrix. Then,…

Q: IF A is a nonzero n X n matrix such that A 0, then A is singular. %3D Select one: True False

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Q: 36) Prove that if A is an invertible matrix and B is row equiva- lent to A, then B is also…

A: You will find solution in next step

Q: ) Consider the matrix A = [a b] with a, b, c and d real-valued numbers. Under which condition(s) for…

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Q: Give an example of a 2 x 2 matrix A such that im(A) =ker(A). %3D

A: Null space of a linear transformation: T:V(F)→V'(F) be a linear transformation then the null space…

Q: If A is an nxn matrix with det(A)=0, then the homogeneous system Ax = 0 has infinitely many…

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Q: Is it true or false? If A is nxn matrix, c is scalar, then cA |=c | A| Birini seçin:

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Q: If you know all 16 cofactors of a 4 by 4 invertible matrix A, how would you find A?

A: Given, an invertible square matrix A of order 4, and we know all the 16 cofactors of this matrix.…

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

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Q: If A is an invertible matrix. Then det(AA-): 1D

A: IA is an invertible matrix To find det(AA-1)

Q: b) Consider the matrix A = [a b] with a, b, c and d real-valued numbers. Under which condition(s)…

A: Negative definite: A square matrix is said to be negative definite if all the eigenvalues of the…

Q: Prove that if A is an invertible matrix and B is row equiva- to A, then B is also invertible. ation

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Q: Suppose that x and y are mxn matrices. Prove that xT- yT=(X -YT. Find a 2x2matrix A, that is not the…

A: Take A and B as arbitrary m×n matrices and evaluate the left and right sided expression

Q: A = (ai j )is a 3 × 3 matrix, develop the general ex-pression for det(A) by expanding(a) along the…

A: Given: Let A=aij be a 3×3 matrix.  To determine: The general expression for det(A) by expanding  a)…

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: 2. If A is 3 x3 matrix such that A 1 then A is -4 diagonalizable. Select one: True False

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Q: Show that if A is any m × n matrix, then AAT and AT A are symmetric.

A: There is a matrix  A given of order m×n. To show that AAT  and  ATA  are symmetric. Solution: The…

Q: 2. If A is an upper triangular matrix and B is a lower triangular matrix, then ((AT)-- 2B)- is : O A…

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Q: Suppose that A is a 5 x 5 matrix which has a null space of dimension 4. The rank of A is rank(A) =

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Q: If A is 3 x 3 matrix such that (A + I3)² = 0 %3D Show that: A is invertible.

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Q: Suppose A is a matrix that is 0 0 0 0 0 0 0 0 0 What is I-A

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

A: Introduction: It is the sum of the diagonal elements of the matrix from upper left to lower right.…

Q: If A is an m × n matrix of rank r, what are the dimensions of N(A) and N(AT )? Explain.

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Q: Let Q be an m xn matrix with n >n and orthonormal columns, then we have both QTQ = I, and QQT = Im…

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Q: Show that if A is an m × n matrix such that AAT is non- singular, then rank A = m.

A: Let AAT can be non singular only if the columns in A are linear independent and they span the column…

Q: Suppose A-A, where A is the matrix. The det (A) is

A: Determinant of a null matrix is equal to zero.

Q: IF A is a nonzero n X n matrix such that A = 0, then A is singular. Select one: O True False

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Q: 3 Let be 4mxn & Bnxm Matrixes that meet: AB = 1 m Prove that to the homogeneous system Bx = 0 There…

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Q: Let A be an n × n matrix with a column of zeros. Show directly from the Leibniz formula that…

A: Let, A be an n×n matrix with a column of zeros.  To prove detA=0 using Leibnitz formula for…

Q: A square matrix is skew-symmetric when AT = −A. Prove that if A is an n × n skew-symmetric matrix,…

A: It is given that A is a skew symmetric matrix.

Q: If a is skew symmetric nxn matrix and n is odd,prove that det A = 0.

A: Consider a skew symmetric n x n matrix A where n is odd. Here the objective is to prove that det(A)…

Q: 1. Find the matrix P that projects points in the plane onto the line 5x - 2y = 0

A: As per honor code, we are entitled to solve only one question at a time so I am providing the same.…

Q: For a nonsingular matrix A and nonzero scalar k, show that (kA)-1 = A-1.

A: For a nonsingular matrix A and nonzero scalar K To show that kA-1=1kA-1 Consider a non singular…

Q: An n x n matrix A is invertible if ВА In АВ II

A: Inverse Matrix: Let A be an n × n matrix. If there exists an n × n matrix B such that AB = I = BA,…

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: A Hessenberg matrix H, is n x n matrix that has 2 on the main diaonal, 1 everywhere below the main…

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Q: Let A be a nilpotent matrix of order n then A*n = 0 ) nxA = 0 A =nx1, l is Identity matrix

A: A be a nilpotent matrix of order n

Q: Consider 1 A = 2 2 1 1 3 -1 -3 4 Convert A to an upper triangular matrix U by using Gaussian…

A: We have to convert the matrix A=121213-1-34 into an upper triangular matrix U by using Gaussian…

Q: If an upper triangular matrix A is singular then at least one diagonal element is zero. O True O…

A: We have to find out

Q: If A is a skew-symmetric matrix then show that AAT = AT A and A² is symmetric. [Note AT denotes the…

A: We will use definition

Q: Show that if B is a symmetric nonsingular matrix, then B2 is positive definite.

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: Let A be an m x n matrix. Prove that if B can be obtained from A by anelementary row [column]…

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Q: If A is an invertible matrix and det(A) = 7, what is det (A-1)?

A: Given: If A is an invertible matrix and det(A) = 7 To find: what is det (A-1 )?