Linear Algebra Examples

Popular Problems
Linear Algebra
Simplify the Matrix 3[[0,0,2],[3,1,0],[0,-2,4]]-2[[0,2,1],[3,0,5],[7,-6,0]]+8[[1,-1,2],[3,4,5],[0,1,-1]]-4[[0,25,12,5],[6,75,8,75,7,5],[-3,5,3.5,-1]]
3[0023100-24]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]3⎡⎢⎣0023100−24⎤⎥⎦−2⎡⎢⎣0213057−60⎤⎥⎦+8⎡⎢⎣1−1234501−1⎤⎥⎦−4⎡⎢⎣02512567587575−353.5−1⎤⎥⎦
Step 1
Multiply 3 by each element of the matrix.
[3⋅03⋅03⋅23⋅33⋅13⋅03⋅03⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]
Step 2
Simplify each element in the matrix.
Tap for more steps...
Rearrange 3⋅0.
[03⋅03⋅23⋅33⋅13⋅03⋅03⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange 3⋅0.
[003⋅23⋅33⋅13⋅03⋅03⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange 3⋅2.
[0063⋅33⋅13⋅03⋅03⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange 3⋅3.
[00693⋅13⋅03⋅03⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange 3⋅1.
[006933⋅03⋅03⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange 3⋅0.
[0069303⋅03⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange 3⋅0.
[00693003⋅-23⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange 3⋅-2.
[0069300-63⋅4]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange 3⋅4.
[0069300-612]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]
[0069300-612]-2[0213057-60]+8[1-1234501-1]-4[02512567587575-353.5-1]
Step 3
Multiply -2 by each element of the matrix.
[0069300-612]+[-2⋅0-2⋅2-2⋅1-2⋅3-2⋅0-2⋅5-2⋅7-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]
Step 4
Simplify each element in the matrix.
Tap for more steps...
Rearrange -2⋅0.
[0069300-612]+[0-2⋅2-2⋅1-2⋅3-2⋅0-2⋅5-2⋅7-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange -2⋅2.
[0069300-612]+[0-4-2⋅1-2⋅3-2⋅0-2⋅5-2⋅7-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange -2⋅1.
[0069300-612]+[0-4-2-2⋅3-2⋅0-2⋅5-2⋅7-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange -2⋅3.
[0069300-612]+[0-4-2-6-2⋅0-2⋅5-2⋅7-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange -2⋅0.
[0069300-612]+[0-4-2-60-2⋅5-2⋅7-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange -2⋅5.
[0069300-612]+[0-4-2-60-10-2⋅7-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange -2⋅7.
[0069300-612]+[0-4-2-60-10-14-2⋅-6-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange -2⋅-6.
[0069300-612]+[0-4-2-60-10-1412-2⋅0]+8[1-1234501-1]-4[02512567587575-353.5-1]
Rearrange -2⋅0.
[0069300-612]+[0-4-2-60-10-14120]+8[1-1234501-1]-4[02512567587575-353.5-1]
[0069300-612]+[0-4-2-60-10-14120]+8[1-1234501-1]-4[02512567587575-353.5-1]
Step 5
Multiply 8 by each element of the matrix.
[0069300-612]+[0-4-2-60-10-14120]+[8⋅18⋅-18⋅28⋅38⋅48⋅58⋅08⋅18⋅-1]-4[02512567587575-353.5-1]
Step 6
Simplify each element in the matrix.
Tap for more steps...
Rearrange 8⋅1.
[0069300-612]+[0-4-2-60-10-14120]+[88⋅-18⋅28⋅38⋅48⋅58⋅08⋅18⋅-1]-4[02512567587575-353.5-1]
Rearrange 8⋅-1.
[0069300-612]+[0-4-2-60-10-14120]+[8-88⋅28⋅38⋅48⋅58⋅08⋅18⋅-1]-4[02512567587575-353.5-1]
Rearrange 8⋅2.
[0069300-612]+[0-4-2-60-10-14120]+[8-8168⋅38⋅48⋅58⋅08⋅18⋅-1]-4[02512567587575-353.5-1]
Rearrange 8⋅3.
[0069300-612]+[0-4-2-60-10-14120]+[8-816248⋅48⋅58⋅08⋅18⋅-1]-4[02512567587575-353.5-1]
Rearrange 8⋅4.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624328⋅58⋅08⋅18⋅-1]-4[02512567587575-353.5-1]
Rearrange 8⋅5.
[0069300-612]+[0-4-2-60-10-14120]+[8-8162432408⋅08⋅18⋅-1]-4[02512567587575-353.5-1]
Rearrange 8⋅0.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008⋅18⋅-1]-4[02512567587575-353.5-1]
Rearrange 8⋅1.
[0069300-612]+[0-4-2-60-10-14120]+[8-816243240088⋅-1]-4[02512567587575-353.5-1]
Rearrange 8⋅-1.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]-4[02512567587575-353.5-1]
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]-4[02512567587575-353.5-1]
Step 7
Multiply -4 by each element of the matrix.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[-4⋅0-4⋅25-4⋅12-4⋅5-4⋅6-4⋅75-4⋅8-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
Step 8
Simplify each element in the matrix.
Tap for more steps...
Rearrange -4⋅0.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-4⋅25-4⋅12-4⋅5-4⋅6-4⋅75-4⋅8-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
Rearrange -4⋅25.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-4⋅12-4⋅5-4⋅6-4⋅75-4⋅8-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
Rearrange -4⋅12.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-4⋅5-4⋅6-4⋅75-4⋅8-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
Rearrange -4⋅5.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-4⋅6-4⋅75-4⋅8-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
Rearrange -4⋅6.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-4⋅75-4⋅8-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
Rearrange -4⋅75.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-4⋅8-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
Rearrange -4⋅8.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-4⋅75-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
Rearrange -4⋅75.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-4⋅7-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
Rearrange -4⋅7.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-4⋅5-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
Rearrange -4⋅5.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-20-4⋅-3-4⋅5-4⋅3.5-4⋅-1]
Rearrange -4⋅-3.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-4⋅5-4⋅3.5-4⋅-1]
Rearrange -4⋅5.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-4⋅3.5-4⋅-1]
Rearrange -4⋅3.5.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-14-4⋅-1]
Rearrange -4⋅-1.
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
[0069300-612]+[0-4-2-60-10-14120]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Step 9
Add the corresponding elements.
[0+00-46-29-63+00-100-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Step 10
Simplify each element of the matrix [0+00-46-29-63+00-100-14-6+1212+0].
Tap for more steps...
Simplify 0+0.
[00-46-29-63+00-100-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify 0-4.
[0-46-29-63+00-100-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify 6-2.
[0-449-63+00-100-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify 9-6.
[0-4433+00-100-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify 3+0.
[0-44330-100-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify 0-10.
[0-4433-100-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify 0-14.
[0-4433-10-14-6+1212+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify -6+12.
[0-4433-10-14612+0]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify 12+0.
[0-4433-10-14612]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
[0-4433-10-14612]+[8-81624324008-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Step 11
Add the corresponding elements.
[0+8-4-84+163+243+32-10+40-14+06+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Step 12
Simplify each element of the matrix [0+8-4-84+163+243+32-10+40-14+06+812-8].
Tap for more steps...
Simplify 0+8.
[8-4-84+163+243+32-10+40-14+06+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify -4-8.
[8-124+163+243+32-10+40-14+06+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify 4+16.
[8-12203+243+32-10+40-14+06+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify 3+24.
[8-1220273+32-10+40-14+06+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify 3+32.
[8-12202735-10+40-14+06+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify -10+40.
[8-1220273530-14+06+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify -14+0.
[8-1220273530-146+812-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify 6+8.
[8-1220273530-141412-8]+[0-100-48-20-24-300-32-300-28-2012-20-144]
Simplify 12-8.
[8-1220273530-14144]+[0-100-48-20-24-300-32-300-28-2012-20-144]
[8-1220273530-14144]+[0-100-48-20-24-300-32-300-28-2012-20-144]
 [x2  12  √π  ∫xdx ]