Matrices

|A| not equal to zero

0

|A| = 0

ALL

a) $$A$$   can be reduced to a matrix in REF which does not have a zero row.

b) $$A$$   can be reduced to the zero matrix i.e. the $$n\times n$$  matrix whose every entry is 0.

c) $$\det A\ne0$$  .

d) Any system of linear equations whose LHS is represented by $$A$$  has a unique solution.

$$\left(1,5\right)$$  

$$\left(5,-1\right)$$  

$$\left(5,1\right)$$  

$$\left(-1,5\right)$$  

(e)

(b)

(d)

(c)

(a)

  $$\Delta$$  Z $$\ne$$   0

$$\Delta$$  X $$\ne$$  0

  $$\Delta$$ $$\ne$$   0

$$\Delta$$  Y  $$\ne$$  0

A

B

C

D

[[-2, 1], [1.5, -0.5]]

[[4, 3], [2, 1]]

[[1, 0], [0, 1]]

[[2, -1], [-3, 1]]

No Inverse Exists