Question

7-3 Let S be the parallelogram determined by the vectors by = were [ 1 ] 7[ 3.7) comes let A= Compute the area of the image of S under the mapping XHAX. -2 3 The area of the image of Sunder the mapping X-Axis (Type an integer or a decimal.)

Answer 1

To solve this problem we use the fact that the area of a parallelogram spanned by two vectors is the magnitude of the cross product between the two vectors.Please thumbs up my answer.

Given transformation is A=17 - 3 L-2 3 Given that, s is spanned by. 6,1 .b, 2 [-59 5+(-15)) P-50 ..Ab - 13-046 Les Ab- 31310420 -1 34 - 35+ (-26)] 5-59 . Image of Sis spanned by Ab, and Abz We know that area of a parallelo gream spanned by two vector is the magnitud of cross product of the vector. Now, Ab, x Abaz li jk. - 50 25. o -5.9 34 o = (-50x34 +59 +25) - (1700+1475) = - 225k .:11 Ab, x Aball = 225 -The required area of parallelogram (il image of 5) under mapping at Ax is 225 square units