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Disc9 - Math 17B Kouba Discussion Sheet 9 1 Consider the...

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Unformatted text preview: Math 17B Kouba Discussion Sheet 9 1.) Consider the following matrices of various dimensions. Perform the indicated opera- tions. 10—-1 210 A: 1 2 0 ,B= 01 2 ,C=(;"f),D=(;‘j i) 0—23 10—2 2 -2 E=(1—1 0 4), F: 3 —1 a.) 30 b.) A — B c.) B’, the transpose of B d.) CD e.) AB f.) BA g.) EF h.) FE i.) Compute 0—1, the inverse of C j.) Compute A“, the inverse of A. sic—3,123 2.) Con51der the system { 23: + 3y 2 26 a.) Solve the system usingmatrix reduction. b.) Rewrite the system in the form. AX = B and solve it using A‘l. 3.) Compute the determinant of each of the following matrices to determine which matrices are invertible. If the matrix is invertible, determine its inverse matrix. a.)A=<; ‘43) b-)A=<.23 :16) C-)A=((1) (1)) d')A=(g g) 4.) Determine the inverse for each 31:3 matrix. 1 0 3 2 —-1 3 3 1 4 a.)A= 2 —1 1 b.)A:= .1 1. —1 c.)A= 416 0 1 «2 3 —2 1 1 0 1 . $+3z=2 5.) Use your answer in part 4.)a.) to solve the system { 2m — y + z = —3 11—2220 30 —14 2 3 7.) LetA—(0 O)’ 6.) Let A = (1 _2> and B = ( 5 0) Show that AB is not equal to BA. 0 0 a.) Find a 2x2 matrix B so that AB = (0 0 ), or explain why it is impossible. b.) Find a 2x2 matrix B, where NOT ALL of the entries are zero, so that AB = (8 8), or explain why it is impossible. 0 1.4 1.8 2.7 0.9 0.9 0 0 0 0 8.) Consider the Leslie matrix L = 0 0.75 , 0 O O 0 0 0.6 0 0 0 0 0 0.4 0 a.) How many age classes are in this population ? b.) What percenatge of 2—year old females survive to the end of the following breeding season ? c.) What percenatge of 4-year old females survive to the end of the following breeding season ? d.) What is an average number of female offspring for a 0—year old female ? e.) What is an average number of female offspring for a 1-year old female ? f.) What is an average number of female offspring for a 3-year old female ? 1000 650 g.) If N(0) = 450 , determine N(1) . 550 300 “ I hear and I forget. I see and I remember. I do and I understand.”— Chinese Proverb ...
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