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# Tutorial 4 - and Cramer’s Rule 3 3 2 2 3 2 1 1 2 1 k x x...

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Tutorial 4 – Introduction to Calculus and Linear Algebra Page 1 of 1 Tutorial 4 Introduction to Calculus and Linear Algebra In Exercises 1 to 6, given A , find A –1 , if it exists. You may try row operations or determinant and cofactor approaches. Check each inverse by showing A –1 A = I . 1. 1 0 9 1 2. - - 5 2 2 1 3. - - 3 2 7 5 4. 6 2 9 3 5. - - - - 1 1 0 1 1 1 0 1 1 6. Write the following systems as a matrix equation and solve using matrix inverse method and Cramer’s Rule. 2 2 1 1 2 1 5 2 2 k x x k x x = + = - - where 2 , 3 ) ( 1 , 4 ) ( 5 , 2 ) ( 2 1 2 1 2 1 - = - = = - = = = k k C k k B k k A 7. Write the following systems as a matrix equation and solve using matrix inverse method
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Unformatted text preview: and Cramer’s Rule. 3 3 2 2 3 2 1 1 2 1 k x x k x x x k x x = +-=-+-=-where , 2 , 3 ) ( 4 , , 1 ) ( 2 , 1 , 1 ) ( 3 2 1 3 2 1 3 2 1 =-= =-= =-= = = = k k k C k k k B k k k A 8. For n x n matrices A and B and n x 1 matrices C , D , and X , solve each matrix equation below. (i) AX = BX +C (ii) X + C = AX - BX 9. Encode the message “CAT IN THE HAT” with the matrix       = 2 1 5 3 A . 10. Decode the following message by the matrix A given in Exercise 10 above. 111 43 40 15 177 68 50 19 116 45 86 29 62 22 121 43 68 27...
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