Matrices - Find Inverse from Simplified Augmented Matrix (3x3) (Level 1)

Math worksheet on 'Matrices - Find Inverse from Simplified Augmented Matrix (3x3) (Level 1)'. Part of a broader unit on 'Matrices' Learn online: app.mobius.academy/math/units/matrices/

Find the inverse of this augmented matrix by doing the required row operations

$A LaTex expression showing \left[ {\begin{array} {cccc} -4 & 0 & 0 & \vert & 1 & 0 & 0 \\ 0 & 0.5 & 0 & \vert & 0 & 1 & 0 \\ 0 & 0 & -0.5 & \vert & 0 & 0 & 1 \end{array} } \right]$

a $A LaTex expression showing \left[ {\begin{array} {ccc} 0.38 & 0 & 0 \\ 0 & -3 & 0 \\ 0 & 0 & 3 \end{array} } \right]$

b $A LaTex expression showing \left[ {\begin{array} {ccc} -0.25 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & -2 \end{array} } \right]$

d $A LaTex expression showing \left[ {\begin{array} {ccc} 0.21 & 0 & 0 \\ 0 & -0.03 & 0 \\ 0 & 0 & 0.03 \end{array} } \right]$

e $A LaTex expression showing \left[ {\begin{array} {ccc} 0.25 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 2 \end{array} } \right]$

f $A LaTex expression showing \left[ {\begin{array} {ccc} -0.5 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & -4 \end{array} } \right]$

Find the inverse of this augmented matrix by doing the required row operations

$A LaTex expression showing \left[ {\begin{array} {cccc} 1 & 0 & 0 & \vert & 1 & 0 & 0 \\ 0 & 0 & 4 & \vert & 0 & 1 & 0 \\ 0 & 4 & 0 & \vert & 0 & 0 & 1 \end{array} } \right]$

b $A LaTex expression showing \left[ {\begin{array} {ccc} 2 & 0 & 0 \\ 0 & 0 & 0.5 \\ 0 & 0.5 & 0 \end{array} } \right]$

c $A LaTex expression showing \left[ {\begin{array} {ccc} -1.25 & 0 & 0 \\ 0 & 0 & -0.31 \\ 0 & -0.31 & 0 \end{array} } \right]$

d $A LaTex expression showing \left[ {\begin{array} {ccc} -0.5 & 0 & 0 \\ 0 & 0 & -0.12 \\ 0 & -0.12 & 0 \end{array} } \right]$

e $A LaTex expression showing \left[ {\begin{array} {ccc} 1 & 0 & 0 \\ 0 & 0 & 0.25 \\ 0 & 0.25 & 0 \end{array} } \right]$

f $A LaTex expression showing \left[ {\begin{array} {ccc} -1 & 0 & 0 \\ 0 & 0 & -4 \\ 0 & -4 & 0 \end{array} } \right]$

Find the inverse of this augmented matrix by doing the required row operations

$A LaTex expression showing \left[ {\begin{array} {cccc} 0 & -2 & 0 & \vert & 1 & 0 & 0 \\ -3 & 0 & 0 & \vert & 0 & 1 & 0 \\ 0 & 0 & 1 & \vert & 0 & 0 & 1 \end{array} } \right]$

a $A LaTex expression showing \left[ {\begin{array} {ccc} 0 & -0.33 & 0 \\ -0.5 & 0 & -1 \\ 0 & 1 & 1 \end{array} } \right]$

b $A LaTex expression showing \left[ {\begin{array} {ccc} 0 & 12 & 0 \\ 18 & 0 & 0 \\ 0 & 0 & -6 \end{array} } \right]$

c $A LaTex expression showing \left[ {\begin{array} {ccc} 0 & 2 & 0 \\ 3 & 0 & 0 \\ 0 & 0 & -1 \end{array} } \right]$

d $A LaTex expression showing \left[ {\begin{array} {ccc} 0 & 0.18 & 0 \\ 0.27 & 0 & 0 \\ 0 & 0 & -0.09 \end{array} } \right]$

e $A LaTex expression showing \left[ {\begin{array} {ccc} 0 & -0.33 & 0 \\ -0.5 & 0 & 0 \\ 0 & 0 & 1 \end{array} } \right]$

f $A LaTex expression showing \left[ {\begin{array} {ccc} 0 & -0.25 & 0 \\ -0.38 & 0 & 0 \\ 0 & 0 & 0.75 \end{array} } \right]$

Find the inverse of this augmented matrix by doing the required row operations

$A LaTex expression showing \left[ {\begin{array} {cccc} 3 & 0 & 0 & \vert & 1 & 0 & 0 \\ 0 & 1 & 0 & \vert & 0 & 1 & 0 \\ 6 & 0 & 1 & \vert & 0 & 0 & 1 \end{array} } \right]$

a $A LaTex expression showing \left[ {\begin{array} {ccc} 0.17 & 0 & 0 \\ 0 & 0.5 & 0 \\ -1 & 0 & 0.5 \end{array} } \right]$

b $A LaTex expression showing \left[ {\begin{array} {ccc} 2 & 4 & 2 \\ 3 & 9 & 6 \\ 2 & 8 & 3 \end{array} } \right]$

c $A LaTex expression showing \left[ {\begin{array} {ccc} -1.5 & 0 & 0 \\ 0 & -0.5 & 0 \\ -3 & 0 & -0.5 \end{array} } \right]$

d $A LaTex expression showing \left[ {\begin{array} {ccc} -0.5 & 0 & 0 \\ 0 & -1.5 & 0 \\ 3 & 0 & -1.5 \end{array} } \right]$

e $A LaTex expression showing \left[ {\begin{array} {ccc} -0.08 & 0 & 0 \\ 0 & -0.25 & 0 \\ 0.5 & 0 & -0.25 \end{array} } \right]$

f $A LaTex expression showing \left[ {\begin{array} {ccc} 0.33 & 0 & 0 \\ 0 & 1 & 0 \\ -2 & 0 & 1 \end{array} } \right]$

Find the inverse of this augmented matrix by doing the required row operations

$A LaTex expression showing \left[ {\begin{array} {cccc} 0 & -3 & 0 & \vert & 1 & 0 & 0 \\ 3 & 0 & 0 & \vert & 0 & 1 & 0 \\ 0 & 0 & 1 & \vert & 0 & 0 & 1 \end{array} } \right]$

a $A LaTex expression showing \left[ {\begin{array} {ccc} 0 & -27 & 0 \\ 27 & 0 & 0 \\ 0 & 0 & 9 \end{array} } \right]$

b $A LaTex expression showing \left[ {\begin{array} {ccc} 0 & 0.33 & 0 \\ -0.33 & 0 & 0 \\ 0 & 0 & 1 \end{array} } \right]$

c $A LaTex expression showing \left[ {\begin{array} {ccc} 0 & -0.1 & 0 \\ 0.1 & 0 & 0 \\ 0 & 0 & 0.03 \end{array} } \right]$

d $A LaTex expression showing \left[ {\begin{array} {ccc} 0 & -0.21 & 0 \\ 0.21 & 0 & 0 \\ 0 & 0 & 0.07 \end{array} } \right]$

e $A LaTex expression showing \left[ {\begin{array} {ccc} 2 & 9 & 9 \\ 5 & 0 & 4 \\ 4 & 0 & 5 \end{array} } \right]$

f $A LaTex expression showing \left[ {\begin{array} {ccc} 0 & -0.17 & 0 \\ 0.17 & 0 & 0 \\ 0 & 0 & -0.5 \end{array} } \right]$

Find the inverse of this augmented matrix by doing the required row operations

$A LaTex expression showing \left[ {\begin{array} {cccc} 1 & 8 & 0 & \vert & 1 & 0 & 0 \\ 0 & 4 & 0 & \vert & 0 & 1 & 0 \\ 0 & 0 & 1 & \vert & 0 & 0 & 1 \end{array} } \right]$

a $A LaTex expression showing \left[ {\begin{array} {ccc} 4 & 32 & 0 \\ 0 & 16 & 0 \\ 0 & 0 & 4 \end{array} } \right]$

b $A LaTex expression showing \left[ {\begin{array} {ccc} -0.06 & -0.5 & 0 \\ 0 & -0.25 & 0 \\ 0 & 0 & -0.06 \end{array} } \right]$

c $A LaTex expression showing \left[ {\begin{array} {ccc} 0.05 & 0.42 & 0 \\ 0 & 0.21 & 0 \\ 0 & 0 & 0.05 \end{array} } \right]$

d $A LaTex expression showing \left[ {\begin{array} {ccc} 1.25 & -2.5 & 0 \\ 0 & 0.31 & 0 \\ 0 & 0 & 1.25 \end{array} } \right]$

e $A LaTex expression showing \left[ {\begin{array} {ccc} 1 & -2 & 0 \\ 0 & 0.25 & 0 \\ 0 & 0 & 1 \end{array} } \right]$

f $A LaTex expression showing \left[ {\begin{array} {ccc} 0.11 & 0.89 & 0 \\ 0 & 0.44 & 0 \\ 0 & 0 & 0.11 \end{array} } \right]$

Find the inverse of this augmented matrix by doing the required row operations

$A LaTex expression showing \left[ {\begin{array} {cccc} 2 & 0 & 0 & \vert & 1 & 0 & 0 \\ 0 & 2 & 0 & \vert & 0 & 1 & 0 \\ 6 & 6 & 1 & \vert & 0 & 0 & 1 \end{array} } \right]$

a $A LaTex expression showing \left[ {\begin{array} {ccc} 8 & 0 & 0 \\ 0 & 8 & 0 \\ 24 & 24 & 4 \end{array} } \right]$

c $A LaTex expression showing \left[ {\begin{array} {ccc} -0.25 & 0 & 0 \\ 0 & -0.25 & 0 \\ 1.5 & 1.5 & -0.5 \end{array} } \right]$

d $A LaTex expression showing \left[ {\begin{array} {ccc} -0.38 & 0 & 0 \\ 0 & -0.38 & 0 \\ 2.25 & 2.25 & -0.75 \end{array} } \right]$

e $A LaTex expression showing \left[ {\begin{array} {ccc} 0.5 & 0 & 0 \\ 0 & 0.5 & 0 \\ -3 & -3 & 1 \end{array} } \right]$

f $A LaTex expression showing \left[ {\begin{array} {ccc} 0.14 & 0 & 0 \\ 0 & 0.14 & 0 \\ 0.43 & 0.43 & 0.07 \end{array} } \right]$

Practice:

Find Inverse from Simplified Augmented Matrix (3x3)

Matrices - Find Inverse from Simplified Augmented Matrix (3x3) Worksheet