1) The statement “The transpose of an upper triangular matrix is a lower triangular matrix” true or false? explain

2) If A is an n × n nonsingular matrix, then which of the following statement is false? explain

a)A is invertible

b)Ax=0 has trivial solution

c)Ax=b has a unique solution for every n × 1 matrix b

d)Ax=0 has nontrivial solution

3) If in a linear system in 2 equations in 2 unknowns has no solution, what does the graph represents? explain

5) In three-dimensions, if the equation of the planes intersects in a point then the solution of the system will be what?explain

6) linear equation in two-dimensions is an equation of a what?explain

7)The sum of a diagonal matrix and an upper triangular matrix is a what? explain

8)

Which of the following equation is not linear in x, y, and z? explain

a)x-√2y+z^a+1=1, a=1

b)x-y+cz+1=0, c=1/2

c)x+2y-4z=1

d)5x+6y+z^b=0, b=1/2