.Let matrix A = 1 2 3 6 Write the vector u = (4, 3) as u = ur + un where ur and un belong to the row space and nullspace of A, respectively

Q: 1] Suppose that W, N are non-zero two- dimensional vectors which are not parallel. Show that if C is…

A: Please rate and feel free to ask any query about any part of the question

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of P 1 - b ]

A: Let w= [x y ] is a stable vector of the given matrix.  So, the equations to solve are:

Q: First change the given pattern into a vector w of zeros and ones by turning each shaded square into…

A: Given w=1110 We have to find the M Let M=m1m2m3m4 Since, w=1110 then wT=1110

Q: 27. Consider an n × m matrix A, a vector v in R", and a vector w in R". Show that (Av) · w = i · (A™…

A:

Q: If Q = I - auu" where Qis an orthogonal matrix, a > 0, and u E R"X1 real vector, and I is n x n…

A:

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 x and y be vectors in Rn and let Q be an n × n orthogonal matrix. Show that if z = Qx and w = Qy…

A:

Q: 1.2.4 Prove that vectors (1, 1, 1)", (2, 1,0)", (3, 1, 4)", and (1, 2, –2)" are linearly dependent.…

A: Let v1, v2, v3 and v4 are given vectors that is v1=111  ,  v2=210 , v3=314 and v4=12-2 Claim:    v1…

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: where En is a k-dimensional vector, A e Ckxk is a constant matrix, and B : Z+ Ckxk is a matrix…

A: Given,      tn+1-t¯=∑i=01αi(tn-i-t¯)+∑i=01βi(zn-i-z¯)…

Q: c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real…

A: A be a matrix 5 * 5  We have to find the matrix A and also find the geometric description of A and…

Q: Consider the following matrix and vector: 1 1 A = 1 -4 0 -3 -2 and x = 6

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Q: 5. Suppose us v and w are linearly independent vectors. Prove that (i) и+у - 2w, и — v — w, и+ w are…

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Q: 5. The four matricesSx,Sy,Szand I are defined bySx=(0 11 0),Sy=(0−ii0),Sz=(100−1),I=(1 00…

A: Given that  Sx=0110, Sy=0-ii0 ,Sz=100-1 ,I=1001 First it is required to show that  Sx2=I and…

Q: Suppose A is (\m \times n \) matrix that has r pivots, then the null space of A contains only the…

A: Option A will be the right answer.

Q: 1.2.5 If a, b, and c are linearly independent vectors in R", prove that a+b, b+c, and a + c are also…

A:

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector - [';" - a 1 - ] a P = b

A: From the given information, P=1-aab1-b Let, stable vector as, w=xy

Q: The equatiokn  Y = (x,y)T  is given as a vectorfunction with 2 components and A = table below 3 2 2…

A: Given is a matrix A and we have to diagonalize the matrix A. First we find eigenvalue of matrix A…

Q: The four matrices Sx, Sy, S and I are defined by 0 -1 where i2-1. Show that S I and SS iS,, and…

A:

Q: solve using the concept of rank.

A: Given set of vectors is: S = {[4     1     2], [2      5      -5], [2      -1        3]} We have to…

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: Suppose M is the set of all real column vectors in R' whose components are equal, then the basis for…

A: See the detailed solution below.

Q: 3) Let B, = {u,, u2} and B2 = {v,, v3} be the bases for R° in which u, = (1,2), uz= (2, 3), v =…

A: The solution is given as

Q: Let A be an n × n matrix and let x and y be vectors in Rn. Show that if Ax = Ay and x /= y, then the…

A:

Q: linear algebra question:

A: The orthogonal projection is given by,

Q: deal with the problem of solving Ax = b when det A = 0.22.Suppose that, for a given matrix A, there…

A: Looks like you copied some part of the previous question together with this one.   Answering:…

Q: Show that if the non-zero vectors s(1), s(2),..., s(m) are conjugate to a positive definite matrix…

A: We are given that the non-zero vectors s(1), s(2), ..., s(n) are conjugate to a positive definite…

Q: Let x1,...,xk be linearly independent vectors in Rn, and let A be a nonsingular n×n matrix. Define yi…

A: Given that,   Let x1,...,xk be linearly independent vectors in Rn, and let A be a nonsingular n×n…

Q: 4 Suppose v1, V2, V3 are vectors in R*, and the matrix A = v, v2 V3 has rank 1 W = Span{v1, V2, V3}…

A:

Q: Let A be an n x n Hermitian matrix and X and Y be n x 1 column vectors. Prove that (AX)·Y – X ·(AY)=…

A:

Q: Write down the 3 by 3 matrix A whose entries are(a) aij = minimum of i and j(b) aij = (-1)i+j(c) aij…

A: I have solved all the three parts one by one. Please pay attention to the steps.

Q: Let r1, .. r,be vectors in R", and let Q be an m xn matrix. Write the matrix Qr, Qr, as a product of…

A: Given:Let r1.......rp be vectors in ℝnLet Q be an m×n matrix Qr1.......QrpR=r1.......rpQ=Q…

Q: 2 Consider A = -2 null(A). 4 2 2 4 -4 -2 -2 -4 -2 0 1 Give a set of vectors that spans each of im(A)…

A:

Q: Generate a matrix A by settingA = floor(10 ∗ rand(6))and generate a vector b by settingb = floor(20…

A: Generate a matrix by setting A = floor(10*rand(6)) and a vector b by setting b = floor(20*rand(6,1))…

Q: 5. Let x and y be vectors in R" and let Q be an n x n orthogonal matrix. Show that if z = Qx and w =…

A:

Q: the norms of a vector X = [1,12, ...,I" and matrix A = (a5) are respectively defined as ||X|| = E…

A: Given, the norms of a vector                     X=x1, x2, . . ., xnTand matrix…

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: Suppose that A is a square matrix and that ∥Au∥ = 1 for all unit vectors u. Show that A is…

A: Given: To show that A is orthogonal, assuming that A is a square matrix. Here Au =1for all unit…

Q: Suppose masses m1, m2, m3, m4 are located at positions x1, x2, x3, x4 in a line and connected by…

A: (a) The 4 x 4 matrix equation relating the column vectors f and x will be:

Q: If P is the projection matrix onto the line through () -- (;) C) and ) then I – P projects onto the…

A: I have checked one by one option wise

Q: First change the given pattern into a vector w of zeros and ones by turning each shaded square into…

A: M = 0 will be the right answer.

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of 1 - a а P = 1 - b [ W =

A:

Q: 7. Show that 3-{(; ) ( ) ( )} -1 2 S = 2 1 6 9 is linearly dependent in M22. Write one of the…

A: According to our guidelines I solve only 1 question, so kindly request you to repost the remaining…

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

A:

Q: let A be an mxn matrix and v and w vectors in Rn. If v and w were both solutions to Ax=0, show that…

A:

Q: Show that for matrices A, B E RXn, a vector w = ABx can be written as w = E,(b{ x)a;, %3D :D1 where…

A: Since, A,B∈ℝn×n. ∴ A, B have 'n' rows and 'n' columns with entries as real numbers. The given vector…

Q: c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real…

A:

Q: S. The image of the vector i + j – 2k under a mapping (1 2 3 defined by the matrix M, where M = 0 1…

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.