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In Exercises 1-12, find the products AB and BA to determine whether B is the multiplicative inverse of A.
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ALGEBRA+TRIGONOMETRY
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- Solve each of the following equations by finding [ a ]1 and using the result in Exercise 9. a.[ 4 ][ x ]=[ 5 ]in13b.[ 8 ][ x ]=[ 7 ]in11c.[ 7 ][ x ]=[ 11 ]in12d.[ 8 ][ x ]=[ 11 ]in15e.[ 9 ][ x ]=[ 14 ]in20f.[ 8 ][ x ]=[ 15 ]in27g.[ 6 ][ x ]=[ 5 ]in319h.[ 9 ][ x ]=[ 8 ]in242 Let [ a ] be an element of n that has a multiplicative inverse [ a ]1 in n. Prove that [ x ]=[ a ]1[ b ] is the unique solution in n to the equation [ a ][ x ]=[ b ].arrow_forwardRather than use the standard definitions of addition and scalar multiplication in R3, let these two operations be defined as shown below. (a) (x1,y1,z1)+(x2,y2,z2)=(x1+x2,y1+y2,z1+z2) c(x,y,z)=(cx,cy,0) (b) (x1,y1,z1)+(x2,y2,z2)=(0,0,0) c(x,y,z)=(cx,cy,cz) (c) (x1,y1,z1)+(x2,y2,z2)=(x1+x2+1,y1+y2+1,z1+z2+1) c(x,y,z)=(cx,cy,cz) (d) (x1,y1,z1)+(x2,y2,z2)=(x1+x2+1,y1+y2+1,z1+z2+1) c(x,y,z)=(cx+c1,cy+c1,cz+c1) With each of these new definitions, is R3 a vector space? Justify your answers.arrow_forwardFor each of the following pairs of matrices A, B calculate the products AB and BA, if they exist. a) A?? = [1 2] [ -1 3], B = [0 3] [2 -4] b) A = ? [−2 −1] [1 0] ? , B = [1 0 5 ][2 4 3] c) A ?= [1 0 2] [3 -1 4] [2 1 3] , B? = [412] [101] [320] * imagine in matrix set up 1st bracket is first row of numbers and so on.arrow_forward
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