Please tell me what happen here the question is :
If A is an n×n matrix with the property that Ax =
0
for all x ∈ Rn, show that A = O. Hint: Let x = ej
for j = 1, . . . , n
Please tell me what happen here the question is : If A is an n×n matrix...
Please follow the comment If A is an n×n matrix with the property that Ax = 0 for all x ∈ Rn, show that A = O. Hint: Let x = ej for j = 1, . . . , n.
Please explain with example: follow the comment: If A is an n×n matrix with the property that Ax = 0 for all x ∈ Rn, show that A = O. Hint: Let x = ej for j = 1, . . . , n. Why ej=(1,....n) then it comes out it is a column vector and all zero except 1 inside, i don't get it Ax = 0 for all XEO" Let A-(a,a,. Let e.-| | | ← jth element...
I don't understand why there is ei equal all 0 but 1 will appear in the middle , please give me some example with this matrix to explain it Given that A is an n×n matrix with the property AX = 0 for all X " 1 A=(a,,a,, 0 0 Let a.) Let e, =| | | ← ith element Comment
Matrix notation: A=(a1,a2,a3.....,an) = [a1 a2 a3 a4 .....an] are they equal? look at the sample picture A should be matrix but it uses ( ) rather than [ ] Given that A is an n×n matrix with the property AX = 0 for all X " 1 A=(a,,a,, 0 0 Let a.) Let e, =| | | ← ith element Comment
LINEAR ALGEBRA: PLEASE FOLLOW THE COMMENT and please tell me what is the rotate matrix and why there is cos@ and -sin@ i think it should be cos@ and sin@ on the first row For each of the following linear operators on R2, find the matrix representation of the transformation with respect to the homogeneous coordinate system: (a) The transformation L that rotates each vector by 120◦ in the counterclockwise direction (b) The transformation L that translates each point 3...
please help if you know Optimization with Quadratic Functions Could you please prove 89. Thank you so much ! Quadratic Functions A quadratic function is a mapping Q R R that is a scalar combination of single variables and pairs of variables. Thus, there are coefficients Cli,] and Ell, and a real number q, such that for X E IRn, we have The m atrix notation for C is suggestive. Indeed, C is n × n, and we take E...
Linear algebra: tell me what happen. How do we get that matrix A by using the D derivative D(x^2)=2x how we get D(x^2)=2x+0*1???? follow the comment EXAMPLE 5 The linear transformation D defined by D(p-p' maps P3 into P2. Given the ordered bases [r.x, and [x, for Ps and P2, respectively, we wish to determine a matrix representation for D. To do this, we apply D to each of the basis elements of P3 Convert t Microso Documen D(x) =...
Please show all work in READ-ABLE way. Thank you so much in advance. Problem 2.2 n and let X ε Rnxp be a full-rank matrix, and Assume p Note that H is a square n × n matrix. This problem is devoted to understanding the properties H Any matrix that satisfies conditions in (a) is an orthogonal projection matriz. In this problem, we will verify this directly for the H given in (1). Let V - Im(X). (b) Show that...
Let A be an m × n matrix, let x Rn and let 0 be the zero vector in Rm. (a) Let u, v є Rn be any two solutions of Ax 0, and let c E R. Use the properties of matrix-vector multiplication to show that u+v and cu are also solutions of Ax O. (b) Extend the result of (a) to show that the linear combination cu + dv is a solution of Ax 0 for any c,d...
Plese help me!!!(Conditioning of Problems and Stability of Algorithms) IA is an m x n matrix, and x is an n x 1 vector, then the linear transformation У-Ax maps Rn to Rm, so the linear transformation should have a condition number, condAar (x). Assume that ||l is a subordinate norm. a. Show that we can define condAx (x) = 11All 11제/IAxl for every x 0. IA is an m x n matrix, and x is an n x 1...