help me answer this question of elementary linear algebra please
help me answer this question of elementary linear algebra please Suppose T R2 R3 is a...
Consider the linear transformation T: R3 + R2 defined as T(X1, X2, 23)=(-23, -3 &1 – 23). Write the standard matrix for HoT, where H is the reflection of R2 about the y-axis. ab sin (a) a дх f a 12 ?
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined by x1 + 5x2 – x3 T(x) - X2 x1 + 2x3 Let B be the standard basis for R3 and let B' = {V1, V2, V3}, where 4 4. ---- 4 and v3 -- 4 Find the matrix of T with respect to the basis B, and then use Theorem 8.5.2 to compute the matrix of T with respect to the basis B”....
Let x = [xı x2 x3], and let TER → R be the linear transformation defined by T() = x1 + 6x2 – x3 -X2 X1 + 4x3 Let B be the standard basis for R2 and let B' = {V1, V2, V3}, where 7 7 and v3 = 7 V1 V2 [] --[] 0 Find the matrix of I with respect to the basis B. and then use Theorem 8.5.2 to compute the matrix of T with respect to...
Let T be the linear transformation from R3 into R2 defined by (1) For the standard ordered bases a and ß for R3 and IR2 respectively, find the associated matrix for T with respect to the bases α and β. (2) Let α = {x1 , X2, X3) and β = {yı, ys), where x1 = (1,0,-1), x2 = - (1,0). Find the associated (1,1,1), хз-(1,0,0), and y,-(0, 1), Уг matrices T]g and T12
linear algebra Determine whether the function is a linear transformation. T: R2 R3, T(x, y) = (x,xy, vy) O linear transformation O not a linear transformation
For real non-zero constants a and b, consider the linear transformation T: R3 + R3 defined by orthogonal reflection in the plane ay + b2 = 0 where orthogonality is defined with respect to the dot product on R3 x R3. Find in terms of a and b the numerical entries of the matrix Aſ that represents T with respect to the standard ordered basis {el, C2, C3} of R3.
For real non-zero constants a and b, consider the linear transformation T: R3 + R3 defined by orthogonal reflection in the plane ay + b2 = 0 where orthogonality is defined with respect to the dot product on R3 x R3. Find in terms of a and b the numerical entries of the matrix Aſ that represents T with respect to the standard ordered basis {el, C2, C3} of R3.
Linear Algebra 1. Consider the following map T : R2 → R. Is T a linear transformation? Explain 2. Suppose that A is a 3 × 4 matrix. The following elementary row operation has the same effect as multiplying a matrix E on the left of A. What is that matrix E?
Assume that T is a linear transformation. Find the standard matrix of T T R3-R2 T (el) : (19), and T (e2): (-6,4), and T (e)-9-7), where el e2 and e3 are the columns of the 3x3 identity matrix A(Type an integer or decimal for each matrix element.)
Please help me to solve those problems. 17. Define a linear transformation from R2 to R3 by T(x1, x2) = (x1 - X2, X1 + 2x2,2x2). a. Give the standard matrix of T. b. Is there an X e R so that T(x) = (1,1,2)? 18. Let A = {{ }]. Which of [ 211, [3] and () are eigenvectors of A? 19. For the matrix -21 4 -1 1 0 -1 2 , find the cofactors C22 and C14....