ebra MTAS Consider the linear transformation T: R4 R2 defined as T(*1,42,43,44)=(-22 - 3 x3 +2...
Consider the linear transformation T: R4 + R2 defined as T(11,12,13,14)=(-221 +22 +2 14,322 -14) Find the standard matrix for T: ab sin(a) f 8 a 12 . ar What is the dimension of ker(T)? Number Is T one-to-one? Enter one yes no Write the standard matrix for HoT, where H is the reflection of R2 about the line y=1. ab sin(a) f αο α Ω TI д
Consider the linear transformation T : R2 + R2 defined as T(21,12)=(0,21 – 12). Find the standard matrix for T: a ab sin(a) 8 f E д 0 0 1 What is the dimension of ker(T)? Is T one-to-one? no 47 Enter one: yes no Write the standard matrix for HoT, where H is the reflection of R2 about the z-axis. a ab sin(a) f 12 II 8 R ат
R2 defined as Consider the linear transformation T: R2 T(21,22)=(0,21 – 22) Find the standard matrix for T: a ab sin (a) f 8 ат What is the dimensi of ker(T)? Is T one-to-one? Enter one: yes no Write the standard matrix for HoT, where H is the reflection of R2 about the 3-axis. a sin(a) f 22 8 R a E är (Alt + 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 T R3 R4 be the linear transformation defined by T(π1, Ο2, 73) - ( 3α1 -4 , X3, 12.x2 3.x3, 6x1-25x3, 10x2 + 10x3) (a) Determine the standard matrix representation of T (b) Find a basis for the image of T, Im(T), and determine dim(Im(T)) (c) Find a basis for the kernel of T, ker(T), and determine dim(ker(T))
Find a matrix M such that the linear transformation T : R5 + R4 defined by T(x) = Mx has the property that its kernel, ker(T), is given by ker(T) € R5 | t1 - 3r2 = 0, z3 - 2c4 = 0 and z5 = 0 C5. and its range, R(T), is given by -{1: - -{{:) == ལྟ་ ༢༠༡༧ - R(T) =
Find a matrix M such that the linear transformation T:R5 → R4 defined by T(x) = Mx has the property that its kernel, ker(T), is given by ker(T) {1: ER5 @1 - 3c2 = 0, c3 - 2c4 = 0 and c5 and its range, R(T), is given by R(T) - {(:) - ༠ ༠ ༠ ༡ e R4 | u + c + + ཀྱ =
I need help with the last part of this question (ie: Write the standard matrix for H∘T, where H is the reflection of R2 about the line y=x.) Consider the linear transformation T: R4_R2 defined as T(11,12,13,14)=(-211 +12 +214,-312-14). Find the standard matrix for T: sina) a dr f -2 1 0 2 -3 0-1 2 What is the dimension of ker(T)? Is T one-to-one? NO Enter one: yes no Write the standard matrix for HoT where H is the...
Let T: R4 → R3 be the linear transformation represented by T(x) = Ax, where 1 A = 0 -2 1 0 1 2 3 . 0 0 1 0 (a) Find the dimension of the domain. (b) Find the dimension of the range. (C) Find the dimension of the kernel. (d) Is T one-to-one? Explain. O T is one-to-one since the ker(T) = {0}. O T is one-to-one since the ker(T) = {0}. O T is not one-to-one since...
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.