1-If x= [ 2 6 12; 15 6 3; 10 11 1], then a) replace the first row elements of matrix x with its average value. b) reshape this matrix into row vector.

Q: Suppose A = PRP–1, where P is orthogonal and R is upper triangular. Show that if A is symmetric,…

A: According to the given information suppose, It is required to show that if A is symmetric then R is…

Q: Show that there is no matrix A E M250x250 with real entries satisfying AAT = -I.

A: Given that A is real ( All entries are real)  square matrix of order 250×250. The trace of any real…

Q: Show that if the entries in each row of an n × n matrix A add up to zero, then the column vectors of…

A: linearly dependent means det of A is zero

Q: Find a (2x2) singular matrix A that maps (2, 4) into (3, 1).

A: Singular matrix mean its Determinant is equal to 'zero' .

Q: and = %3D are oignualus of a matrix A Corraspondeng to the egnualuong=2 and >=-2 then = ACTa t Ja)=…

A: For a given matrix A if 'x' is eigen vector of matrix A corresponding to the eigen value ' q ' then…

Q: Suppose A is an m x n matrix whose columns are linearly independent. What is the nullity of A?

A: Given A is an m×n matrix whose columns are linearly independent. We have to find the nullity of A.

Q: Consider the following LP: marz = 5x1 + x2 + 2r3 s.t. I1 +12 + 13 <6 6x1 + +x3 < 8 x2 +13 < 2 I1,L2,…

A: Hi! you have posted multiple subparts. As per the norm, we have solved the first 3 subparts. If you…

Q: Let A and B be n × n nonsingular matrices. Find nonsin- gular matrices P and Q so that PAQ = B.

A: Given that A and B  are n×n non singular matrices. An n×n matrix A is non singular only if A is…

Q: Let A be square matrix. If A" = 0. A= Oava %3D for n> 2. Then

A:

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

A:

Q: 3.- Consider the following matrix [20 8 -4] A = -8 4 8 10 6 20 Which choice will be the correct…

A:

Q: If A is a real n xn matrix, show that AA" and ATA are similar. (Hint. Start with an SVD for A.)

A:

Q: 3. 3 If A is non singular matrix whose mverse 2. Al = fad A.

A:

Q: 3.2. Determine, if the vectors (9000 (:) (3) 1 1 1 1 1 1 1 1 are linearly independent or not. Do…

A: To determine a set of vector is linearly independent then determinant must be non zero.

Q: Suppose that A and B are matrices having n rows. Prove that M(A|B) = (MA|MB) for any m ×n matrix M.

A:

Q: Suppose that collA) = IR+ 4x7 matrix A has 4 lead terms Then and NCA) = R³ %3D %3D

A:

Q: Suppose a 5x4 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space…

A: Multiple :    Let  A be 5 × 4 matrix . We have given that , rankA = 3. We need to find , dimension…

Q: (2) Let A = UDV" be a SVD of a square matrix A. What is the sum of squares of the singular values,…

A: We find the sum of squares of the singular values in terms of A.

Q: The Matrix B from 3 x 2 at b = 1- - is %3D 1. 2. 3.

A:

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: If the rows of an n X n matrix A are linearly inde­pendent as vectors in Rn, what is the rank of A?…

A:

Q: 4 It is known that the system Ax = b is consistent, where A E Mmxn. Define a matrix BE Mmx(n+1) as B…

A: A matrix Ax=b  and A is a column matrix then A is consistent iff b can be written in the linear…

Q: Let A be a 7 × 5 matrix of rank 4. Let P and Q be theprojection matrices that project vectors in R7…

A:

Q: Suppose A is anmxn matrix whose columns are linearly independent. What is the nullity of A?

A:

Q: Let the n × n matrix A be equal to AT . Briefly describe the pattern of the entries in A.

A: Consider the matrix A of order n×n such that AT=A. let, A=a11a12…a1na21a22…a2n⋮⋮⋱⋮an1an2…ann  here…

Q: 4. Let martix A is any (mxn) matrix and let B is a square matrix. Show that, any vector 'b' chosen…

A: Given: Matrix A is (MxN) Matrix B is square and diagonal matrix Vector B is coloumn space of matrix…

Q: Let A = UEVT be a SVD of a square matrix A. What is the product of the diagonal elements of E, in…

A:

Q: 2 4. Find the matrix A satisfying A and A 1 and write the SVD of A in vector form. [Hint: Start by…

A:

Q: Suppose that A is an invertible matrix with n columns, and entry aij in row i and column j. 1.…

A: Let matrix is A and the entries are aij .

Q: If the null space of a 7 x 6 matrix A is 5-dimensional, what is the dimension of the column space of…

A: We solve given problem with the help of rank nullity theorem

Q: 2. Let the rref of a matrix A be, 0 2 0 -2 0 1 -5 0 -3 0 0 0 1 6 Determine A if the first, second…

A:

Q: 6) Find the SVD of the matrix by manually calculating U 4 11 14 A = 8 7 -2]

A:

Q: Suppose that Ax=b has no solution and the columns of A are linearly independent. Let t(A) denote the…

A: This is a problem of Linear Transformation.

Q: If A is a square matrix whose rows add up to the zero vector, explain why A cannot be invertible.

A: Given A is square matrix whos rows add up to zero vector.

Q: 3- If x=[ 26 12; 15 6 3; 10 11 1], then a) replace the first row elements of matrix x with its…

A: X=[  2 6 12;15 6 3;10 11 1]

Q: If the rows of an mxn matrix A are linearly independent and Ax=b is consistent then it has unique…

A:

Q: 3. Choose the matrix that is equal to the matrix below. 0.82 2 12 4 5 9 19 082 2 0.6 [B] 12 4 10 3…

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Q: 22. Construct a 3 × 3 matrix A, with nonzero entries, and a vector b in R³ such that b is not in the…

A: Detailed explanation mentioned below

Q: Either the row vectors or the column vectors of a square matrix are linearly independent. True False

A: Any row vectors or column vectors of a square are said to be linearly independent if…

Q: Determine the matrix C such that (CT – 21) 1 1 2 2 3

A:

Q: Show that if A is an n × n matrix, then det(AAT ) ≥ 0.

A: Given, A is a n x n matrix. Let AT be the transpose of A. To prove det (AAT) is non-negative.

Q: O Find the transforma tion matrix that wotates the axis X of a rec tangu lar coor dinale system 60…

A:

Q: If A is an n×n matrix and {v1,v2,…,vn}    is a linearly independent set of vectors in Rn, then…

A: This is true

Q: Let A be an m × n matrix. Show that ATA and AAT are both symmetric.

A: Given A be an m×n matrix. we have to show that ATA and AAT are both symmetric.we will make use of…

Q: 2. Choose the rank of the matrix AT

A:

Q: 3) If x=[2 6 12; 15 6 3; 10 11 11, then: a) Replace the first row elements of matrix x with its…

A:

Q: Let A be a matrix and mathbfb be a matrix and a vector defined by 1 -1 b : 1 3 Compute x* that…

A:

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

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.