Here is my question:
Give a matrix B, determine the invertibility of B by examining the column vectors of B.
I have solved this one way, by trying to show that the column vectors are independent, by computing the determinant of the matrix B, if it is NON-Zero then for this situation of being a homogeneous system, then we get that we have the trivial solution, which means the coefficients of the system of vectors based on the columns of the matrix B are all zero, which means the vectors are independent.
I dont know if this question allows you to compute the determinant. If we are not allowed, how else can one show that the columns are independent. Do we need to perform row-echelon form reduction on the matrix. Also the very specific matrix that was given, the first element of this 3x3 has a zero.
Hope someone can tell me how to go about showing this.