Linear Equations and Matrices

Question 1

What are the possible outcomes for solutions of a system?

Answer 1

No solution
A unique solution
Infinitely many solutions

Question 2

What is a homogeneous system?

Answer 2

When b1=b2=…=bm=0 (RHS of a system, =b column)

Question 3

What does m and n in an mxn matrix?

Answer 3

m = no. of rows
n = no. of columns

Question 4

In a matrix multiplication of A(mxn) and B(axb) , when will the result be undefined?

Answer 4

When m=/=b

Question 5

In a matrix multiplication of A(mxn) and B(axb), what will be the dimensions of the product matrix?

Answer 5

nxa

Question 6

Is matrix multiplication commutative?

Answer 6

Nope, B.A != A.B

Question 7

When is a matrix in echelon form?

Answer 7

All row consisting of only zeros are at the bottom
First non-zero number in any row is ‘1’
Successive non-zero rows begin with more zeros left of the ‘1’ then the rows above

Question 8

What is a consistent solution?

Answer 8

When the solution to a system is either unique or infinitely many

Question 9

What is an inconsistent solution?

Answer 9

When there is no solution to a system