3- If x=[ 26 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: Construct a 3 x 3 triangular matrix A so that 1] the vector 2 is in Col A. 3]

A: We know every lower or upper traingular matrix is a triangular matrix.

Q: 7. Use matrices to stretch the vector horizontally by a factor of 3.

A:

Q: b) Determine the matrix A for the linear transtormation which means that the vectors Of the room are…

A:

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: 2. Find a vector orthogonal to the nullspace of the matrix [1 27 6. 4 L5 -1 2.

A: According to the given information it is required to find a vector orthogonal to the null space of a…

Q: Write the row space and the null space of the matrix Г1 2 3 |4 5 6 7 8 9 as a span of vectors.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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

A: Given that the n×n non-singular matrices as A and B. It is known that a matrix is non-singular only…

Q: Let A be an m×n matrix. Show that if A has linearly independent column vectors, then N(A) = {0}.

A:

Q: If the kernel of a 5 x 4 matrix A consists of the zero vector only and if Au = Aw for two vectors v…

A: It is an necessary and sufficient condition for one one function

Q: Determine all values of the parameters x and y such that the vector 1 s in the range of the above…

A:

Q: Let A be a 3 x 4 matrix, let y, and y, be vectors in R3, and let w = y, + y2. Suppose y, = Ax, and…

A:

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 and B be n × n matrices and let x be a vector in Rn. How many scalar additions and…

A:

Q: If Q is an orthogonal matrix, prove that any matrix obtained by rearranging the rows of Q is also…

A: The matrix is said to be an orthogonal matrix if the product of a matrix and its transpose gives an…

Q: the matrIX A into a product QDQ" where Q is orthogonal and D is diagonal.

A: Given,          A=-5-1-1-1-3-1-1-1-3

Q: Let A be an 8 × 5 matrix of rank 3, and let b be anonzero vector in N(AT ). Show that the system Ax…

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: 21 Find the matrix that projects a vector from R onto the column space of the matrix 0 12 4

A: Consider the matrix A=120124. Columns of A are 102 and 214 . Clearly, they are linearly independent.

Q: .

A:

Q: Let A be a 2 × 2 matrix with linearly independentcolumn vectors a1 and a2. If a1 and a2 are usedto…

A:

Q: Show that the column vectors of following matrix A are linearly independent:

A: the given question is taken from the matrix in which we have to find show that the given matrix A is…

Q: Show that if A is a mxn matrix and rank(A)=m then Ax=b has a solution for any vector b in Fm (Hint:…

A:

Q: Determine if the column space of the matrix A included contains the vector(11,−9,5,7). If so,…

A: Given below the detailed solution.

Q: 1-If x= [ 2 6 12; 15 6 3; 10 11 1], then a) replace the first row elements of matrix x with its…

A: The average of n digit can be obtained by dividing the sum of the digits by the number of digits…

Q: Let the matrices Ho, H, Ha 1x1 M어ni x [1]. be defined ... the He=L He-I vector of length n-2" can be…

A:

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: Show that if C is a matrix whose columns are the components (x1, y1) and (x2, y2) of two…

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

Q: 4. Determine if the vector b is in the span of the columns of the matrix A, where [1 2 3 A = 7 8 10…

A:

Q: The matrix X1 X = is called a vector.

A: We have to find

Q: Let MS be the n × n matrix whose j th column is v j and let MT be the n × n matrix whose j th column…

A: Given: Here it is given an n×n matrix of Ms whose jth row is Vj as well as an n×n matrix MT whose…

Q: Construct a 3 x 3 matrix A with every entry non-zero such that the following vector b is in the span…

A: See the attachment

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: find if the vector x is in the range for matrix A

A:

Q: -) Let A, B be nx n symmetric matrices such that XTAX = X™BX for all %3D column vectors X e R". Show…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 8. Use matrices to compress the vector vertically by a factor of X-ахis. and reflect it over the

A:

Q: Construct a 3 x 3 nonzero matrix A such that the vector is a solution of Ax = 0.

A: Given conditionAx = 0          .................(1)x = 111 is a solution to Ax=0,Let matrix A be - 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: 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 vector is in the range of a matrix A, then it is also in the null space of A. true of false?

A: Answer

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: 7. Show that the matrix A=I– 2vv' , where v is a unit vector in R", and I is an nxn identity matrix,…

A:

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: 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: 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: Suppose that {v1, v2,..., vn} is a linearly independent set of vectors in Rn. Show that if A is an n…

A: Let's suppose we have a linear relation:…

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: 20. Can every vector in R* be written as a linear combination of the columns of the matrix B above?…

A:

Q: Construct a nonzero 3 × 3 matrix A and a nonzero vector b such that b is in Col A, but b is not the…

A: We will construct A and put b as a linear combination of column vectors in A.

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.