This document provides calculations for matrix operations: 1) AB calculates the product of the given matrices A and B, resulting in the matrix [-3, 1, 5]. 2) BTCT calculates the product of the transposes of matrices B and C, resulting in the matrix [-1, -3]. 3) CA calculates the product of matrices C and A, resulting in the matrix [3, 1, 4; 1, 3, -1]. 4) BBT calculates the product of B and its own transpose, resulting in the matrix [1, -1, 2; -1, 1, -2; 2, -2, 4]. 5) BBT calculates the product of

1. Exercice 29
  
−1 2 0   1
(a) AB =  1

 2 1 −1
 
0 −1 2 2
   
−1(1) + 2(−1) + 0(2) −3
=  1(1) + 2(−1) + 1(2)  =  1
0(1) − 1(−1) + 2(2)
   
5
 
−1 0
(b) BT C T = 1 −1 2  2  1

1 −1
= 1(−1) − 1(2) + 2(1) 1(0) − 1(1) + 2(−1)
= −1 −3
 
−1 2 0
−1 2 1  3 1 4
(c) CA =  1 2 1 =
0 1 −1   1 3 −1
0 −1 2

2. Exercice 29 (suite..)
 
 1
(d) BBT = −1 1 −1 2
 
2
   
 1(1) 1(−1) 1(2)   1 −1 2
= −1(1) −1(−1) −1(2) = −1
   1 −2
2(1) 2(−1) 2(2) 2 −2 4
 
1
T B = 1 −1 2 −1
 
(e) B
2
 
= (1(1) − 1(−1) + 2(2)) = (6)
(f) Pas possible car A3;3 et C2;3 ne sont pas compatibles pour la
multiplication.