Linear Algebra 1. For the following questions first indicate if it\'s True or Fa

Question

Linear Algebra

1. For the following questions first indicate if it's True or False then explain why citing relevant rules or theorems from the textbook. T F (ABCT ATBTCT T F If A and B are 3 × 3 matrices and B = bi b2 bl, then AB = bi Ab2 Ab3 T F A product of invertible n × n matrices is invertible, and the inverse of the product is the product of their inverses in the same order. T F Each column of AB is a linear combination of the columns of B using weights from the corresponding column of A T F The transpose of a sum of matrices equals the sum of their transposes T F If A is invertible, then elementary row operations that reduce A to the identity In also reduce A-1 to In

Explanation / Answer

5.T. The statement is true as (A+B)T = AT + BT.

6. F. If A is invertible, then the elementary row operations that reduce A to In also reduce In to A-1, not vice-versa.

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