Linear Algebra True or False Question 1False 2False 3False 4

Linear Algebra True or False Question

1-False; 2-False; 3-False; 4-True, Im having problems understanding the last ones. Please help

10. There are 8 statements given below with a number to the left of each statement. Create a number from these numbers by selecting all of the statements that are true. For example, if the only true statements are 2, 3 and 5, then create the number 235, and give this as your answer. 1. Suppose A is an mxn matrix and b is an mxl column vector. If the homogeneous system Ax- 0 has infinitely many solutions, then the system Ax- b has infinitely many solutions. 2. Suppose A is an mxn matrix and b is an mxl column vector. The system Ax-b has a unique solution if and only if the homogeneous system Ax- 0 has only the trivial solution 3. Every homogeneous system of linear equations is consistent. 4. A system of linear equations either has no solution, one solution, or infinitely many solutions. 5. There are systems of linear equations with exactly 3 solutions, 6. If a set is linearly independent, and it has 2 or more vectors in it, then the set will still be linearly independent after you remove a vector from it 7. There is a linearly independent subset of R4 that contains 5 vectors. 8. There is a linearly independent subset of R4 that contains only 1 vector.

Solution

5) false as it is exactly three not possible as 4 is true

6) true because if they are linearly indepedent and if you even remove pne from it does not aaffect the dependency of other as it is independent.

7) false cant have more vectors then the power of R

8) true because other can be zero

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