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For each transformation T and basis B and C, find the corresponding matrix representation M of...
Each transformation below is invertible. Determine the closed form representation for the inverse: 1) Let T la +(-1) 6+2c +(-1)d - 1a + 2b + 0c + Od -3a + 56+ (-1) +0d 2a +(-2) b + 3c +0d] с d T-1 2) Let T(a + bx + cx+ dx?) = 1a + 2b + 1c +(-1)d la + 3b + 3c + Od 3a + 7b +6c+(-3) d 8a + 196 +16c+(-6) d 1-[]- 3) Let T 13a +(-17)...
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(1 point) For each transformation below, determine a basis for (Range(T)) Note that if you do not need a basis vector, then write o for entries of that basis vector. For example, if you only need 2 vectors in your basis, then write 0 in all boxes corresponding to the third vector 9 Let 7 [a ] la 250e6d 20 +56 + 10 +14d 2a +65 +2c + 160 4a +(12)+( 4)c+(32) d -30 +...
2) Let T be a linear transformation from P3(R) to M22(R). Let B= (1+2x + 4x2 + 8x3), (1 + 3x + 5x2 + 10x3), (1 + 4x + 7x2 + 13r%),(1 + 4x + 7x2 + 14x²). Let C= [] [ 1];[1 ] [ ] 0 17 40 Let M= 13 31 36 124 22 52 -61 -209 23 55 -64 -220 be the matrix transformation of T from basis B to C. -47 -161 The closed form of...
3) Let T be a linear transformation from M22(R) to P3(R). Let B= (4 5] [1 ] [ 2 1]: [4 ;] Let C = (1 + 1x + 0x2 + Or?),(0+10 + 1x2 + 0x3), (0+ 0x + 1x² + 1r), (0+ 0x + 0x² + 1x2) 1 6 - 2 1 8 -8 18 15 Let M= be the matrix transformation of T from basis B to C. 3 -2 -9 6 -2 -12 5 -41 The closed...
please finish all blanks in 1) 2) and 3)
For each transformation below, find the value of T(U). 1) Let T be a linear transformation from R to M22(R). Let B= 2 5 6 Let C= [ ][ 2 :11; }(31 70 165 -116 273 Let M = 135 -223 -490 -811 be the matrix transformation of T from basis B to C -255 -600 -993 -422 2 Let v= 0 The value of T(U) 2) Let T be a...
For each transformation below, find the value of T(U). 1) Let T be a linear transformation from R$ to M2 (R) 2 Let B= -1 2 3 Let C= [1].[133] [131] 1 -22 -21 -22 -21 -59 14 13 Let M= be the matrix transformation of T from basis B to C 37 -59 30 30 -19 -1 Let v= 2 2 The value of T(0) = 2) Let T be a linear transformation from P3 (R) to M22(R). Let...
For each pair of transformations "T" and "T-1", find T(T-1(w)) and T-?(T()). Then use T or F to indicate if these transformations are inverses of one another. 1) Let T(a + bx + cx2 + dx3) = la +16+(-1)c+ld Da +(-1) b+ 1c +(-1)d la + 2b +(-2) c + 3d 0a + 0 + 0c + 1d and T-1 = 1a +06+1c +0d + (4a + (-4) 6+ (-5) c + 3d) x + (-3a +36 +30 + (-2)...
For each transformation below, find the closed form of the transformation. 1) Let T be a linear transformation from R$ to M22 (R) [i Let B=1 0:00 [. :] [11] [12] [0 ] Let C= 12 41 -17 -5 65 -27 92 Let M = be the matrix transformation of T from basis B to C 17 58 -15 -51 81 The closed form of the transformation is Tb 3-1 2) Let T be a linear transformation from P3(R) to...
Find the matrix of the linear transformation T: V →W relative to B and C. Suppose B = {bı, b2, b3} is a basis for V and C = {C1, C2} is a basis for W. Let T be defined by T(b]) = 261 + C2 T(62) = -501 +502 T(b3) = 2C1-802 2. 3 0 2 -6 [3 0 -6 1 5-8 2 -5 2 5 -8 2 1 -5 5 2 -8
3) Let T be a linear transformation from M22(R) to P3(R). Let B= [11] ]1 2] [3] Let C = (11 + 5x +(-3) 22 +(-1) 23), (13+6x + (-3) x2 + (-2) 2*), (8 + 3x + (-1).x2 + (-2) 23),(-5+(-2) x + 1x2 + 12) Let M= -15 2 -27 -71 28 -4 47 126 -24 5 35 -95 -67 14 -104 -276 be the matrix transformation of T from basis B to C. Let v= [1 The...