-4 1 -1 The rank of the matrix -1 -1 -1 7 -3 1

Can you explain whether a 2×2 matrix with an entire row of zeros can have an inverse?

Explain the difference between the row-echelon form and the reduced row-echelon form of a matrix.

15. Reverse the elementary row operations used in Example 2.9 to show that we can convert

The two matrices A and B are row-equivalent. A=[240171112119121213516481162] B=[120032001053000117000000] (a) Find the rank of A. (b) Find the basis for the row space of A. (c) Find the basis for the column space of A. (d) Find the basis for the null space of A. (e) Is the last column of A in the span of the first three columns of A? (f) Are the first three column s of A linearly independent? (g) Is the last column of A in the span of columns 1, 3, and 4? (h) Are the columns 1, 3, and 4 linearly dependent?

We can add (or subtract) two matrices only if they have the same ______.

Determine whether the matrix is in row-echelon form. If it is, determine whether it is in reduced row-echelon form. 1024011130000

What is the row-echelon form of a matrix? What is a leading entry?

Can a matrix with zeros on the diagonal have an inverse? If so, find an example. If not, prove why not. For simplicity, assume a 22 matrix.

Solve the homogeneous linear system corresponding to the coefficient matrix. [121200242412]