SOLUTION: Could you please take the time to help me solve this question: Suppose A is a 2 x 3 matrix, where its first row consists of 1, 2, and 0, and its second row consists of 0, 2, and 1.

Algebra ->  Matrices-and-determiminant -> SOLUTION: Could you please take the time to help me solve this question: Suppose A is a 2 x 3 matrix, where its first row consists of 1, 2, and 0, and its second row consists of 0, 2, and 1.      Log On


   

Question 101340: Could you please take the time to help me solve this question: Suppose A is a 2 x 3 matrix, where its first row consists of 1, 2, and 0, and its second row consists of 0, 2, and 1. Find the transpose of A, i.e., AT, then multiply A by its transpose, i.e., A AT and finally find the inverse matrix of their product.
Thank you, very much for taking the time to help me, most appreciated
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given matrix
A=%28matrix%282%2C3%2C1%2C2%2C0%2C0%2C2%2C1%29%29


Find the transpose of A by flipping each entry over the diagonal. In other words, the entry in the first row and second column switches with the entry in the second row and first column. So in general a%5Bij%5D=a%5Bji%5D where i and j are the row and column numbers

A%5ET=%28matrix%283%2C2%2C1%2C0%2C2%2C2%2C0%2C1%29%29


Now multiply the two matrices





Now find the determinant of the previous matrix. Remember, if A=%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29, the determinant of matrix A is det%28A%29=a%2Ad-b%2Ac

det%28A%29=5%2A5-4%2A4=25-16=9


Now find the inverse through this formula:

A=%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29===>A%5E-1=%281%2Fdet%28A%29%29%28matrix%282%2C2%2Cd%2C-b%2C-c%2Ca%29%29