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QUESTION 1. §1.9 THE MATRIX OF A LINEAR TRANSFORMATION Le t T R be the linear...
: Question 5. (20 pts) Let T : R² + R be a linear transformation such...
: Question 5. (20 pts) Let T : R² + R be a linear transformation such that T(21,02) = (1 - 2.62,-01 +3.62, 3.01 - 2.2). (1). Find the standard matrix of T (call it A). (2). Is T one-to-one? Justify your answer. (3). Is T onto? Justify your answer.
Question 5. (20 pts) Let T: R² + R* be a linear transformation such that T(21,...
Question 5. (20 pts) Let T: R² + R* be a linear transformation such that T(21, 12) = (x1 - 2x2, -21 +3.22, 3.21 - 202). (1). Find the standard matrix of T (call it A). (2). Is T one-to-one? Justify your answer. (3). Is T onto? Justify your answer.
(1 point) A linear transformation T : R" R whose standard matrix is 1-2 5 -3...
(1 point) A linear transformation T : R" R whose standard matrix is 1-2 5 -3 6 -23+k is onto if and only if k
need help on this. thanks in advance Question 16 Determine whether the linear transformation T is...
need help on this. thanks in advance
Question 16 Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 1-23 -1 3-4 2 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R. One-to-one; not onto #3 One-to-one; onto a Not one-to-one; onto R3 Not one-to-one; not onto a
7. Consider the linear transformation T : (R) → M2x2 (R) defined by ao 2a2 ao-...
7. Consider the linear transformation T : (R) → M2x2 (R) defined by ao 2a2 ao- 3a1 4a0 - 12a1 2ao Find the matrix for T, Ts, where 0 00 00 1 are bases for P2R) and M2x2(R) respectively. Find bases for ker(T) and range(T). Is T one-to-one, onto, neither, or both?
Recall that if T: R" R" is a linear transforrmation T(x) = [Tx, where [T is the transformation matrix, then 1....
Recall that if T: R" R" is a linear transforrmation T(x) = [Tx, where [T is the transformation matrix, then 1. ker(T) null([T] (ker(T) is the kernel of T) 2. T is one-to-one exactly when ker(T) = {0 3. range of T subspace spanned by the columns of [T] col([T) 4. T is onto exactly when T(x) = [Tx = b is consistent for all b in R". 5. Also, T is onto exactly when range of T col([T]) =...
Lett: R R be a linear transformation whose standard matrix is A = 3 9 ....
Lett: R R be a linear transformation whose standard matrix is A = 3 9 . Which of the following 25] statements is true? No work needs to be shown for this question. @ Tis neither one-to-one nor onto Tis onto, but is not one-to-one Tis one-to-one, but is not onto Tis one-to-one and onto
(Note: Each problem is worth 10 points). 1. Find the standard matrix for the linear transformation...
(Note: Each problem is worth 10 points). 1. Find the standard matrix for the linear transformation T: that first reflects points through the horizontal L-axis and then reflects points - through the vertical y-axis. 2. Show that the linear transformation T: R - R whose standard [ 2011 matrix is A= is onto but not one-to-one. - R$ whose standard 3. Show that the linear transformation T: R 0 1 matrix is A = 1 1 lov Lool is one-to-one...
Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T...
Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 37 1 -2 A=-1 3 -4 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R O One-to-one; onto R O Not one-to-one: onto O Not one-to-one; not onto OOne-to-one: not onto
Find the standard matrix of T ( Call it A) Is T one-to-one? Justify your answer...
Find the standard matrix of T ( Call it A)
Is T one-to-one? Justify your answer
Is T onto ? Justify your answer
-> Question 5. (20 pts) Let T : R? R? be a linear transformation such that T(:21,22) = (21 - 222, -21 +3.22, 3.11 - 2:02). (1). Find the standard matrix of T (call it A). (2). Is T one-to-one? Justify your answer. (3). Is T onto? Justify your answer.
: Question 5. (20 pts) Let T : R² + R be a linear transformation such that T(21,02) = (1 - 2.62,-01 +3.62, 3.01 - 2.2). (1). Find the standard matrix of T (call it A). (2). Is T one-to-one? Justify your answer. (3). Is T onto? Justify your answer.
Question 5. (20 pts) Let T: R² + R* be a linear transformation such that T(21, 12) = (x1 - 2x2, -21 +3.22, 3.21 - 202). (1). Find the standard matrix of T (call it A). (2). Is T one-to-one? Justify your answer. (3). Is T onto? Justify your answer.
(1 point) A linear transformation T : R" R whose standard matrix is 1-2 5 -3 6 -23+k is onto if and only if k
need help on this. thanks in advance
Question 16 Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 1-23 -1 3-4 2 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R. One-to-one; not onto #3 One-to-one; onto a Not one-to-one; onto R3 Not one-to-one; not onto a
7. Consider the linear transformation T : (R) → M2x2 (R) defined by ao 2a2 ao- 3a1 4a0 - 12a1 2ao Find the matrix for T, Ts, where 0 00 00 1 are bases for P2R) and M2x2(R) respectively. Find bases for ker(T) and range(T). Is T one-to-one, onto, neither, or both?
Recall that if T: R" R" is a linear transforrmation T(x) = [Tx, where [T is the transformation matrix, then 1. ker(T) null([T] (ker(T) is the kernel of T) 2. T is one-to-one exactly when ker(T) = {0 3. range of T subspace spanned by the columns of [T] col([T) 4. T is onto exactly when T(x) = [Tx = b is consistent for all b in R". 5. Also, T is onto exactly when range of T col([T]) =...
Lett: R R be a linear transformation whose standard matrix is A = 3 9 . Which of the following 25] statements is true? No work needs to be shown for this question. @ Tis neither one-to-one nor onto Tis onto, but is not one-to-one Tis one-to-one, but is not onto Tis one-to-one and onto
(Note: Each problem is worth 10 points). 1. Find the standard matrix for the linear transformation T: that first reflects points through the horizontal L-axis and then reflects points - through the vertical y-axis. 2. Show that the linear transformation T: R - R whose standard [ 2011 matrix is A= is onto but not one-to-one. - R$ whose standard 3. Show that the linear transformation T: R 0 1 matrix is A = 1 1 lov Lool is one-to-one...
Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 37 1 -2 A=-1 3 -4 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R O One-to-one; onto R O Not one-to-one: onto O Not one-to-one; not onto OOne-to-one: not onto
Find the standard matrix of T ( Call it A)
Is T one-to-one? Justify your answer
Is T onto ? Justify your answer
-> Question 5. (20 pts) Let T : R? R? be a linear transformation such that T(:21,22) = (21 - 222, -21 +3.22, 3.11 - 2:02). (1). Find the standard matrix of T (call it A). (2). Is T one-to-one? Justify your answer. (3). Is T onto? Justify your answer.
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