What condition must the matrix $A$ satisfy for every vector $B$ to have a unique solution in $AX = B$?
Question 2
When extending to higher dimensions, why is it easier to solve systems like 9 equations in 9 unknowns with software like MATLAB?
Question 3
Which statement is true about a matrix with linearly dependent columns?
Question 4
What approach will be covered in subsequent lectures to solve systems of equations more systematically?
Question 5
When representing the system of equations as $AX = B$, what does vector $X$ represent?
Question 6
In the given example, which method finds the point of intersection of lines to solve a system?
Question 7
What is an alternative method to matrix-vector multiplication to find the same result?
Question 8
How do you interpret $AX = B$ in the column picture?
Question 9
What result do you get when you multiply the matrix $[[2, 5], [1, 3]]$ by the vector $[1, 2]^T$?
Question 10
Which of the following vectors is part of the columns used in the column picture for the system $AX = B$ with $A = [[2, -1, 0], [-1, 2, -1], [0, -3, 4]]$?
Question 11
Given the matrix equation $AX = B$, what does matrix $A$ represent?
Question 12
What is the solution to the system $2x - y = 0$ and $-x + 2y = 3$?
Question 13
What does the 'row picture' approach in linear algebra focus on?
Question 14
In the context of linear algebra, what does 'invertibility' mean?
Question 15
In the 'column picture' of linear equations, which concepts are primarily addressed?