1. Consider the sets of vectors: A = {(3,6,30),(9,15,81),(-2, – 8, - 34)}, B = {(-1,– 5, – 24),(-4, – 19, – 91),(-6, – 24, – 111)}, Witch form two bases of R. 40 9 - - - - a) Calculate the coordinates...


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1.<br>Consider the sets of vectors:<br>A = {(3,6,30),(9,15,81),(-2, – 8, - 34)},<br>B = {(-1,– 5, – 24),(-4, – 19, – 91),(-6, – 24, – 111)},<br>Witch form two bases of R.<br>40<br>9<br>- -<br>- -<br>a) Calculate the coordinates in the canonical base of R°of the vector V = ( 3 ,3, 2 JA<br>expressed in base A<br>b) Calculate the coordinates of the vector V = (-4,1, – 4) at bases A and B.<br>c) Calculate the base change matrix from B to A<br>d) Consider the vector w given by the coordinates W = (-3,2, – 4), at base B. Calculate the<br>coordinates of this vector at base A.<br>e) Let C be a new base of R3. If the base change matrix, from base A to base Cis<br>- 10<br>55 32<br>35<br>-5<br>3<br>- -<br>-5<br>25<br>21<br>calculate the coordinates of the vector v in section 1 on the base C.<br>

Extracted text: 1. Consider the sets of vectors: A = {(3,6,30),(9,15,81),(-2, – 8, - 34)}, B = {(-1,– 5, – 24),(-4, – 19, – 91),(-6, – 24, – 111)}, Witch form two bases of R. 40 9 - - - - a) Calculate the coordinates in the canonical base of R°of the vector V = ( 3 ,3, 2 JA expressed in base A b) Calculate the coordinates of the vector V = (-4,1, – 4) at bases A and B. c) Calculate the base change matrix from B to A d) Consider the vector w given by the coordinates W = (-3,2, – 4), at base B. Calculate the coordinates of this vector at base A. e) Let C be a new base of R3. If the base change matrix, from base A to base Cis - 10 55 32 35 -5 3 - - -5 25 21 calculate the coordinates of the vector v in section 1 on the base C.

Jun 03, 2022
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