Q. No. 2): 1 4 Let 0 3 1 be the augmented matrix. Denote the columns of A by v, and y, .and -2 6 h-8 W = Span{v,V2}. h=58 1. Check whether "b" lies on the plane Ww = Span{y,v3}.or not? 2. If the above matrix has consistent system then write its solution.

Q: Complete the matrix A so that it is skew-Hermitian. i 2—6і - A = 1 9i Y = = 2

A: Given the matrix, A=0i2-6ix01yz9i The matrix A is said to be skew-Hermitian matrix if, A*=-A Where…

Q: Consider the planes given by the equations x + 2y + 3z = 4 3x + 4y + 5z = 2 5x + 4y + (k - 1)z = k –…

A: This is a non homogeneous system AX=b Concepts required : Infinite solution of the system AX=b will…

Q: b) Given a linear system as below х — 2у + 3z %3 9, —х + Зу %3D — 4, 2х — 5у + 5z %3D 17 Find the…

A:

Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: Given that, the system is- x'=3-20-13-20-13x with x1=et221, x2=e3t-201, x3=e5t2-21.

Q: Given the matrix 2 2 3 1 2 A = 0 2 7 7 Find the |A| by transforming the matrix A to the triangular…

A: Given :A=222023771

Q: Consider the following nonhomogeneous linear system: xi = 2x1 – x2 + t? - x2 = 3x1 – 2x2 + t | 2.…

A:

Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: The wronskian of given system is given as follows :

Q: Consider the following underdetermined matrix form of the system Ax=B, [2 -2 4 -4 A = 5 1 |4 -4 -5…

A: First we need to find the reduced roe echelon form of the augmented matrix (A|B) then by doing back…

Q: 1 3 14. For the vector b=b, to be in the row space of the matrix A= then 256 by . by-4bz +1 lb, = 0…

A:

Q: 1. Consider the following system of linear equations: T1 + kr2 = 2 kri + x2 + 13 =1 X1+ x2 + x3 =k…

A: Here the given matrices are                                      A=abcd and B=dcba We have to show…

Q: 2 . B = 6 : J.c = ( 1. and V = |1. What is the sum of the entries of the [1 Let A %3D 4 5 matrix…

A: We want to find sum of entries of given expression

Q: (a) Find x, y, z and B, where 10 x 3 -3 y 4 4 A = 1 ; A² = 1 ; A² = 1 ; ; c(A+1)+3BT = 2A and I :…

A:

Q: 2. In the linear system Ax = b, A = 1 2 4        2 6 0 b = 27      −4 (a) Show that x = 1…

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

Q: 3: Assume that u, v e R". Let wi = u – v and w2 = u+ v. Show that if u and v are linearly…

A:

Q: 3. Consider the simultaneous equations fi(z, y. 2) = (ry- - 1) = 0, f2(x, y, 2) = (xy² +z2-15y) = 0,…

A: It is given that, f1(x, y, z)=(x2y-z3-1)=0f2(x, y, z)=(xy2-xz2-15y)=0f3(x, y, z)=(2y2+z2-6)=0 The…

Q: Suppose {v1, ..., !,·.., Un} spans R™. Then m 2 n, type ==, or =, into the box on the left. Let A =…

A:

Q: Given that the matrix A has reduced echelon form as follows, answer the following questions. [1 0 [3…

A:

Q: Consider the equation sets below; x + 3y + 2t = 1 z + 4t = 6 x + 3y + z + 6t = 7 a) Write the system…

A: The solution is given as

Q: which of the following M atrices is reduce row echelon form 1 0 31 A = 0 l1 [1 B = 0 1 0 0 01 0 31…

A:

Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A:

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: Consider the system of equations 2x + 3y – z = 0, 2y + z = 1, x – 4y = 2. Which of the following…

A: The system of equation is  2x+3y-z = 02y+z = 1x-4y = 2

Q: 4. Find the coordinates of the vertices of the rectangle WXYZ with coordinates W(0, - 7), X(2, 2),…

A: Here we use the properties of transformation rules of function. In the dilation of a triangle we…

Q: 253 For the linear system AX=B, if A1=1 0 1 and B = %3D 1 2 then the unknowns vector X=

A:

Q: 155. Given three planes x-1.3y-2.4z=-19.30, 3.5x+4.7y+5.8z=78.10, 6.1x-7.2y+8.3z346.50, Determine…

A:

Q: What is the quadratic form of the matrix ( ): O z+zy + y O + O z? + ry +y O2+ zy

A:

Q: 11. Write the system in matrix form x' = 3x – 4y + z + t, y' = x + 2y – z + t?, z' = 6y – 7z + t3

A: Given system is x'=3x-4y+z+t,y'=x+2y-z+t2,z'=6y-7z+t3. Write the system in matrix form.

Q: 1) The curve is a line that passes through the origin . 2) The Matrix a,l.is a column matrix if i =…

A:

Q: For the system below, (b) is not in the column space of Ax = b. 1 4 2 [3 11 3 1- What method should…

A:

Q: 1 2 0 Let A = 12 1 0 h 1 a) For which hare the columns of A linearly dependent? b) For which h is…

A:

Q: (2 -1 5). and that h(T) = T2 – 2T – 7, find h(T). (4) Given matrix A =

A:

Q: . Consider the system of linear equations Ax = b below: x - y - z = 2 2x + 4y + 6z = 8 4x + 2y +…

A: The given system of linear equations Ax = b is, Here, the determinant of the coefficient matrix A…

Q: 3 12 Let y = 10 , and W = Span{u1}. 1 V10 a. Let U be the 2×1 matrix whose only column is u,.…

A: Given :  y = 126 , u1= 310-110 and  W=Span{u1}

Q: Consider the following nonhomogeneous linear system: Y = Y2 + e* Y2 = Y1 – 3e3t - 2.Using MUC, which…

A: Method of Undetermined Coefficient::

Q: 7. Write the given linear system in matrix form and verify that the vector X is a solution of the…

A:

Q: X1 [1 0 2 1 X2 2 and x = 4 1 0 2 A = 3 X3 1 1 3 X4 1 1 -1 -1 0 X5

A:

Q: Suppose {v1,. ..., Un } spans R™. Then m n, type ==, or =, into the box on the left. Let A = 01 Un,…

A:

Q: Given 2 8 -2 -10 -67 [1 4 0 -4 -17 rref 1 4 -2 -6 -5 0 0 1 1 -1 -4 1 5 3 0 0 use the reduced row…

A:

Q: Suppose that a 3x3 matrix A has three columns C1, C2, C3 which span the plane given by x + 2y – 5z =…

A: a) yes the linear system is consistent Since the rank of coefficient matrix is same as the rank of…

Q: 25 3 For the linear system AX = B, if A=1 0 1 and B= 0 1 2) then the unknowns vector X=

A: This question is related to system of linear equations, We will solve it using matrix…

Q: Suppose A=QR, where Q is m×n and R is n× n. Show that if the columns of A are linearly independent,…

A:

Q: Let O be a F.M. of the system Y-4Y on I, where A is 2x2 matrix. Then - [1 2 is also a F 1 3 a) True…

A:

Q: 253 For the linear system AX= B, if A-1=1 0 1 and B= 0 1 2 then the unknowns vector X=

A: Solution:

Q: 4. Find the general solution to the linear system, and then show that the row vectors of the…

A:

Q: Given the matrix 2 2 2 3 1 A = 0 2 7 7 Find the |A| by transforming the matrix A to the triangular…

A: Given :A=222023771

Q: hatate the following triangle uith Q= 45° by the accemate diagram and I final matrix 12 C50,50)…

A:

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

A:

Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A:

Q: Consider the following set of vectors. v, = v, = Let v,, v,, and v, be (column) vectors in R3 and…

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.