Let B be an n x m real matrix with n > m, and let M be the symmetric matrix M = BTB. Note that M is m x m. %3D Show that for any x € R™, x* Mr = ||Bx||3. Show that if B is full-rank, then M is positive definite. Here we assume n=m and that M is positive definite. The matrix B has a QR factorization B = QR, where R is an m x m upper triangular matrir with positive diagonal entries and Q is an orthogonal matrix. Suppose we know M, but we do not know B. What method could we use to get R? (Hint: first figure out the relationship between R and M.)

Q: Given that G is a 1 × 6 matrix and H is a 6 × 1 matrix, a. Is GH defined? If so, what is the order…

A: Given that G is a 1 × 6 matrix and H is a 6 × 1 matrix,a. Is GH defined? If so, what is the order of…

Q: b) Let A be an m × n matrix, and let B be the result of performing a single elementary row operation…

A:

Q: Let X and B be matrices. If we have that B is a symmetric matrix (B is equal to its transposed…

A: Symmetric matrix are those matrix whose transpose is equal to the matrix. Invertible matrix are…

Q: Let A be an n × n matrix and let Q and V be n × northogonal matrices. Show that ||QA ||2 = ||A ||2

A:

Q: Let A be an n X n matrix with n > 1 and suppose A satisfies Ą² - Which one of the following…

A: True of false statement

Q: Let A be a 3 x 3 matrix such that A3 - 6A² + 4A – 31, = 0. Then, A is invertible and A

A:

Q: Suppose that A is an m × n matrix and satisfies the following conditions: dim(row(A)) = 3…

A:

Q: Determine whether the given matrix A is diagonalizable. If so, find a matrix P that diagonalizes A…

A: Given matrix A=01-12 and A=200121-101To find: A matrix P that diagonalizes A and a diagonal matrix…

Q: Let A and B be m x n matrices and || || be any matrix norm for m x n matrices, prove that | || –…

A:

Q: Let A and B be 3 x 3 matrices such that A 3 = B 6 l10! The matrix C = A – 2B is invertible. %3D [5.

A:

Q: Let A be a nonsingular 4 x 4 matrix such that A = -2, then AT adj(A ) Select one: O True O False 17

A: properties of the determinant

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…

A:

Q: Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B= pAP is…

A:

Q: Given a 3x matrix in terms of scalar c and that det (A)=8, find the valuddof G if -1 1c-2 C+7 3. 2.

A:

Q: Let A be an m x n matrix, and let B be an n x m matrix. Show that if m > n, then AB is not…

A:

Q: Suppose A is an n×n matrix ,and let v1,...,vn ∈Rn. Suppose{Av1,...,Avn} is linearly independent.…

A: It is given that {Av1,...,Avn} is linearly independent. We will prove that A is nonsingular.

Q: Consider the following matrix: 1 a A = -1 1 -1 Find the valuc of a E R such that A is…

A:

Q: Let A be an nxn matrix, then for any n EZ*, det( A")= (det A)" . Select one: True False

A:

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

A: Since A is a skew-symmetric matrix we have,  AT=-A where AT is the transpose of matrix A. Then we…

Q: If A is an n × n matrix, show that (Ak )T = (AT )k for any positive integer k.

A: Matrix: We will solve it by the method of induction:(Ak)T=(AT)k case 1: k=1case 2: k=ncase 3: k=n+1

Q: Let A be an m x n matrix. Show that: ( a ) Ifxε Ν (Α'Α), then AxE R(Α) Ω Ν (A"). (b) N (AT A) =…

A: Let A be an  m×n matrix. Show that: (a) If x∈NATA, then Ax∈RA∩NAT (b) NATA=NA. (c) A and AT have…

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: For each matrix A with real valued entries, find a diagonal matrix D and an invertible matrix Q such…

A: These 2 are unrelated lengthy problems,by Chegg policy I have to solve only first one. These 2 are…

Q: Let A be a diagonalizable n x n matrix and let P be an invertible nx n matrix such that B = P-AP is…

A: Given Result: A be a diagonalizable n×n matrix and P be an invertible n×n matrix such that B=P-1AP…

Q: If A be a (n × n) invertible matrix the prove that the Ax = b has exactly one solution.

A: Given- The matrix A be a n×n invertible matrix. To prove- That the Ax=b has exatly oly one solution.…

Q: Let A and B be matrices of size p × m and n × q , respectively. Assume that mn = pq . Define R: Mmn…

A: Matrix A is p×m and B is n×q In a m×n matrix number of element will be m.n R is defined as,…

Q: For the matrix A, find (if possible) a nonsingular matrix P such that PAP is diagonal. (If not…

A:

Q: ^ = [1 ] A If A is diagonalizable, find an invertible 2 x 2 matrix P and a 2 x 2 diagonal matrix D…

A: Given that the matrix A=0-440. If the given matrix is diagonalizable , find an invertible matrix and…

Q: Consider the matrix A of order 4 with a; = (-1)j if i <j and 0 otherwise. Which of the following is…

A: Given : A matrix A of order 4 with    To find the statement true for the matrix A.

Q: Assume that A and B are both n x n matrix. If|AB| + 0, then both A and Bare invertible. O True O…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Let A be an m × n matrix, and let B be the result of performing a single elementary row operation on…

A:

Q: Let A be a m x n matrix, U be a p × m matrix and V be an x p matrix such that VUA= In,where I, is…

A: A square matrix is invertible if and only if the determinant is not equal to zero. Which means ATA…

Q: Give an example of a matrix A such that (1) Ax = b has a solution for infinitely many b e R°, but…

A: If  the dimension of the column space of  A will be 3  (or if A has set of three linearly…

Q: Let A be a 3 x 3 matrix such that A4 - 3A³+ 4A²- 613 = 0. Then, A is invertible and

A: Here we have to use the concept matrix.

Q: Consider M as an n x n matrix, we can say that M is nilpotent  if Mx = 0 for some x ∈ +Z . Now:…

A: (a) Let M be a nilpotent matrix .  So, using definition of nilpotent, Mx=0 for some x∈ℤ+ ⇒Mx=0⇒Mx=0…

Q: Let A be an invertible diagonal matrix. Which of the following is false: O (2A)T = 2 AT If A-1= A,…

A:

Q: Let A be a diagonalizable nx n matrix and let P be an invertible n x n matrix such that B = P-AP is…

A: The complete absolution is in given below

Q: Show that is A is a square matrix, then A + AT is a symmetric matrix. You can use any matrix for A…

A:

Q: Show that if an n × n matrix A is positive definite, then there exists a positive definite matrix B…

A: Consider the provided question,

Q: If G = | is alx1 matrix, and A is a 1xn matrix, is it true that XA = GA for %3D any number A. Is it…

A:

Q: Suppose that A e Mnxn(R) is a positive-definite symmetric matrix. Since A is symmetric, A is or-…

A: We will use the knowledge of standard value decomposition.

Q: Find a 3 x 3 matrix A such that Aa = 9x for all a in R³

A: We have to find matrix A such that Ax = 9x

Q: Let A be an n × n matrix and let B = A + AT and C = A − AT (a) Show that B is symmetric and C is…

A: given: let A be a n×n matrix. B=A+AT C=A-AT we have to show that B is symmetric matrix and C is skew…

Q: Let A be an m × n matrix.(a) Describe the diagonal entries of AT A in terms of the columns of A.(b)…

A: (a) Describe the diagonal entries of AT A in terms of the columns of A.

Q: Let A = [a;;] be the n x n matrix defined by aji = k and a;; = 0 if i + j. Show that if B is any n x…

A: Given: A=aijn×n,     aii=k and aij=0 if i≠k. Let B be a square matrix of order 3 which can be…

Q: Show that if A is any n × n matrix, then (a) A + AT is symmetric. (b) A − AT is skew symmetric.

A: Symmetric matrix: Any matrix A is symmetric matrix if and only if it is equal to its transpose that…

Q: Suppose A is a 3x3 matrix with columns 71, 72, v3 satisfying the following conditions: (i) {V1, U2,…

A:

Q: If A is an n x n symmetric matrix and B is any n x n invertible matrix, prove that A is positive…

A: Consider the given conditions. The A = n × n symmetric matrix and B = n × n invertible matrix.…

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.