a)Find c[Ta]c Dimensions of matrix A are 3 x 3 thus the size of the matrix Ta will also be 3 x 3.
We find the elements of the matrix Ta to be: This is the transpose, Ta. Therefore c(Ta)c where c= 1 0 0 0 1 0 0 0 1 We first get the product of c and Ta after which we will then multiply by matrix c once more. Product c*Ta will yield, 1 0 0 1 0 2 0 1 0 5 2 1 0 0 1 5 7 11 The first matrix is a 3*3 matrix and the second one is also a 3*3 thus the answer should also be a 3*3 matrix. Therefore multiplying the first row of the first row of the first matrix by the first column of the second matrix and so on, we get the product is (1*1)+(0*5)+(0*5) (1*0)+(0*2)+(0*7) (1*2)+(0*1)+(0*11) (0*1)+(1*5)+(0*5) (0*0)+(1*2)+(0*7 (0*2)+(1*1)+(0*11) (0*1)+(0*5)+(1*5) (0*0)+(0*2)+(1*7) (0*2)+(0*1)+(1*11) This will be equal to, 1 0 2 multiplying this by c= 1 0 0 we get the final answer as &nbs; 5 2 1 0 1 0 5 7 11 0 0 1 (1*1)+(0*5)+(0*5) (1*0)+(0*2)+(0*7) (1*2)+(0*1)+(0*11) (0*1)+(1*5)+(0*5) (0*0)+(1*2)+(0*7 (0*2)+(1*1)+(0*11) (0*1)+(0*5)+(1*5) (0*0)+(0*2)+(1*7) (0*2)+(0*1)+(1*11) Thereforec(Ta)c will be, 1 0 2 5 2 1 5 7 11 b) Find c[Ta]b Ta is the transpose of A which is obtained as Dimensions of matrix A are 3 x 3 thus the size of the matrix Ta is also 3 x 3. We find the elements of the matrix Ta to be: This is the transpose, Ta.
The product c[Ta]b will be obtained by: Multiplying c by Ta first we get, we know that c= 1 0 0 and Ta= 1 0 2 p; 0 1 0 5 2 1 0 0 1 5 7 11 This product will be: The first matrix is a 3*3 matrix and the second one is also a 3*3 thus the answer should also be a 3*3 matrix. Therefore multiplying the first row of the first matrix by the first column of the second matrix and so on, we get the product will be (1*1)+(0*5)+(0*5) (1*0)+(0*2)+(0*7) (1*2)+(0*1)+(0*11) (0*1)+(1*5)+(0*5) (0*0)+(1*2)+(0*7 (0*2)+(1*1)+(0*11) (0*1)+(0*5)+(1*5) (0*0)+(0*2)+(1*7) (0*2)+(0*1)+(1*11) = 1 0 2 then multiplying this by matrix b= 2 1 1 5 2 1 1 2 1 5 7 11 1 1 2 The product yields: (2*1)+(1*5)+(1*5) (2*0)+(1*2)+(1*7) (2*2)+(1*1)+(1*11) (1*1)+(2*5)+(1*5) (1*0)+(2*2)+(1*7) (1*2)+(2*1)+(1*11) (1*1)+(1*5)+(2*5) (1*0)+(1*2)+(2*7) (1*2)+(1*1)+(2*11) Therefore c[Ta]b will be; 12 9 16 16 11 15 16 16 25
