Math Problem Solver - Linear algebra examples

Solve using Gaussian Elimination

x_1-2x_2+3x_3=11 4x_1+x_2-x_3=4 2x_1-x_2+3x_3=10

Linear algebra

Find the Cube Roots of a Complex Number

-8i

Linear algebra

Solve using Gaussian Elimination

3x+2y+z=1 5x+3y+4z=2 x+y-z=1

Linear algebra

Solve Using a Matrix by Elimination

-3x+y-z=-2 , -3x+z=4 , y-5z=0

Linear algebra

Simplify the Matrix

R=[[3,2],[-1,0]] , S=[[-2,1],[1,-1]]

Linear algebra

Solve Using a Matrix by Row Operations

x+2y-z=4 , 2x+y+z=-2 , x+2y+z=2

Linear algebra

Solve Using a Matrix by Row Operations

1/2x-y=-3 , 9x-y=1

Linear algebra

Solve using Gaussian Elimination

3x_1+6x_2-6x_3=9 2x_1-5x_2+4x_3=6 -x_1+16x_2-14x_3=-3

Linear algebra

Simplify the Matrix

square root of 50x^2 = square root of 25*2*x^2=5x square root of b

Linear algebra

Solve Using a Matrix by Row Operations

x+3y-z=4 , 3y-z=0 , x-y+5z=0

Linear algebra

Simplify the Matrix

(1,0m^3n^12)

Linear algebra

Solve using Gaussian Elimination

2x_1+4x_2+6x_3=18 4x_1+5x_2-6x_3=24 2x_1+x_2-12x_3=6

Linear algebra

Find the Cube Roots of a Complex Number

1+i

Linear algebra

Simplify the Matrix

Find RS if R=[[3,2],[-1,0]] , S=[[-2,1],[1,-1]]

Linear algebra

Solve Using a Matrix by Row Operations

x-y=9 , x+y=6

Linear algebra

Find the Inverse

[[0,-1,4],[6,0,-2],[1,0,0]]

Linear algebra

Solve using Gaussian Elimination

x_1+x_2-x_3=7 4x_1-x_2+5x_3=4 2x_1+2x_2-3x_3=0

Linear algebra

Find the Cube Roots of a Complex Number

8i

Linear algebra

Find the Null Space

S={[[2],[-1],[3],[1],[2]],[[1],[2],[-1],[5],[2]],[[2],[1],[-3],[6],[1]]}

Linear algebra

Solve using Gaussian Elimination

9x_1+9x_2-7x_3=6 -7x_1-x_3=-10 9x_1+6x_2+8x_3=45

Linear algebra

Find the Null Space

S={[[2],[-1],[3],[1],[0],[3]],[[9],[-6],[-2],[3],[2],[1]],[[1],[1],[1],[0],[0],[1]],[[-3],[1],[4],[2],[1],[2]]}

Linear algebra

Solve using Gaussian Elimination

-2x_1-6x_2-3x_3=9 -x_1+x_2-x_3=1 x_1-x_2+2x_3=2

Linear algebra

Solve using Gaussian Elimination

x+3y-4z=2 3x+10y-12z=8 9x+28y-36z=20

Linear algebra

Solve using Gaussian Elimination

x+y+z=6 2x-y-z=3 x+2y+2z=0

Linear algebra

Solve using Gaussian Elimination

x+y+z=-6 2x+y-z=-1 x-2y+3z=-6

Linear algebra

Solve using Gaussian Elimination

3x_1+6x_2-6x_3=9 2x_1-5x_2+4x_3=6 5x_1+28x_2-26x_3=-8

Linear algebra

Solve using Gaussian Elimination

-2x_1+x_2+6x_3=18 5x_1+8x_3=-16 3x_1+2x_2-10x_3=-3

Linear algebra

Simplify the Matrix

5 cube root of 1,250+7 cube root of 270

Linear algebra

Solve the Matrix Equation

[[32,10],[3/5,1/8]]*F=[[-80,80],[1,2]]

Linear algebra

Simplify the Matrix

square root of x^12y^9z^5 = square root of x^12*y^8*y*z^4*z=x^ay^bz^c square root of yz

Linear algebra

Solve the Matrix Equation

[[1/9,6],[1/3,27]]*B=[[-10,7],[-48,30]]

Linear algebra

Simplify the Matrix

(f(x+h)-f(x))/h , h!=0

Linear algebra

Find Reduced Row Echelon Form

[[-1,0,-2,x_1],[2,3,-1,x_2],[0,-1,-3,x_3]]

Linear algebra

Solve using Gaussian Elimination

2x+6y+z=7 x+2y-z=-1 5x+7y-4z=9

Linear algebra

Solve using Gaussian Elimination

3x-12y+15z=10 -4x+16y-20z=-12

Linear algebra

Simplify the Matrix

(7^2*7^8)/(7^4)=(7^a)/(7^4)=7^b

Linear algebra

Solve using Gaussian Elimination

5x+2y+z=-11 2x-3y-z=17 7x-y=12

Linear algebra

Solve using Gaussian Elimination

2x_1+4x_2+6x_3=18 4x_1+5x_2-6x_3=24 2x_1+x_2-12x_3=2

Linear algebra

Find the Cube Roots of a Complex Number

27i

Linear algebra

Solve using Gaussian Elimination

x_1+2x_2-4x_3=4 -2x_1-4x_2+8x_3=-8

Linear algebra

Simplify the Matrix

[[2],[-6]]-[[-3],[2]]+[[6],[0]]

Linear algebra

Solve using Gaussian Elimination

x+4y=4 2x+9y=11 5x+24y=32

Linear algebra

Solve using Gaussian Elimination

3x+y-z=5 x+2y=8 y-2z=-5

Linear algebra

Find the Square Roots of a Complex Number

4i

Linear algebra

Solve using Gaussian Elimination

4x-3y+z=-8 -2x+y-3z=-4 x-y+2z=3

Linear algebra

Find the Cube Roots of a Complex Number

125i

Linear algebra

Solve Using an Augmented Matrix

2x-3y+z=4 y-2z+x-5=0 3-2x=4y-z

Linear algebra

Solve Using an Augmented Matrix

-2x_1-6x_2-3x_3=9 -x_1+x_2-x_3=1 x_1-x_2+2x_3=2

Linear algebra

Find Reduced Row Echelon Form

[[0,1,-2,1,1,5],[-2,3,-6,0,6,9],[1,1,-2,0,2,3]]

Linear algebra

Find the Square Roots of a Complex Number

3(cos(pi)+isin(pi))

Linear algebra

Find the Fourth Roots of a Complex Number

-4-4i

Linear algebra

Solve the Matrix Equation

x=[[0,2,4,6],[0,3,6,9],[0,4,8,12]]

Linear algebra

Find the Square Roots of a Complex Number

-3+4i

Linear algebra

Find the Fourth Roots of a Complex Number

3(cos(pi)+isin(pi))

Linear algebra

Simplify the Matrix

([(1,4-0,2)*3,2])÷1 , 5

Linear algebra

Find the Cube Roots of a Complex Number

3(cos(pi)+isin(pi))

Linear algebra

Determine if Linearly Dependent

B={[[-1],[4],[7]],[[6],[-5],[8]],[[1],[5],[9]]}

Linear algebra

Determine if Linearly Dependent

[[2],[-1],[4],[1],[2]] , [[1],[2],[-1],[5],[2]] , [[2],[1],[-3],[6],[1]]

Linear algebra

Simplify the Matrix

x/a+x/b=c , a!=0 , b!=0 , a!=-b

Linear algebra

Simplify the Matrix

square root of 2 , square root of 8

Linear algebra

Determine if Linearly Dependent

[[1,2,1],[3,-1,0],[6,-2,0]]

Linear algebra

Determine if Linearly Dependent

[[-1,6,1],[4,-5,5],[7,8,9]]

Linear algebra

Find the Norm

[[4],[0],[4],[5],[6],[7],[8]]

Linear algebra

Determine if Linearly Dependent

[[-1],[4],[7]] , [[6],[-5],[8]] , [[1],[5],[9]]

Linear algebra

Solve using Gaussian Elimination

2x-3y+z=4 y-2z+x-5=0 3-2x=4y-z

Linear algebra

Determine if Linearly Dependent

[[1,2,1],[8,1,10],[6,2,5]]

Linear algebra

Solve Using an Augmented Matrix

3x-5y+z=14 2x+3y-4z=20 5x-y+2z=7

Linear algebra

Find the Square Roots of a Complex Number

4+4i

Linear algebra

Find the Square Roots of a Complex Number

8(cos(pi/2)+isin(pi/2))

Linear algebra

Find the Square Roots of a Complex Number

-4-4i

Linear algebra

Simplify the Matrix

((10x^3y^2)/(5x^-3y^4))^-3 , x!=0 , y!=0

Linear algebra

Find the Norm

[[4],[0],[4],[5],[6]]

Linear algebra

Find the Cube Roots of a Complex Number

8(cos(pi/2)+isin(pi/2))

Linear algebra

Simplify the Matrix

M=((x^5)^0x^8(x^2)^3)/((x*x)^5) , x!=0

Linear algebra

Simplify the Matrix

cube root of 3 , cube root of 24

Linear algebra

Simplify the Matrix

((a^2b^-3)/(a^-2b^2))^2 , a!=0 , b!=0

Linear algebra

Simplify the Matrix

p(x):|5x+1|=-6 q(x):|x-1/2|=2

Linear algebra

Solve using Gaussian Elimination

9x_2-7x_3=2 -x_3=-2 -3x_1+6x_2+8x_3=1

Linear algebra

Find the Fourth Roots of a Complex Number

8(cos(pi/2)+isin(pi/2))

Linear algebra

Simplify the Matrix

(2x+10)/(x^2+x-2)+2/(x+2)+x/(x-1) , x!=-2 , 1

Linear algebra

Solve Using an Inverse Matrix

x+y+z+t=4 , 2x-y-z-t=-1 , x+y-2z=0 , 3x+3t=6

Linear algebra

Find the Cube Roots of a Complex Number

-3+4i

Linear algebra

Simplify the Matrix

[[0,0],[0,0]]-[[x,y],[z,w]]

Linear algebra

Find the Square Roots of a Complex Number

-3+3 square root of 3i

Linear algebra

Solve using Gaussian Elimination

x_1-3x_2+5x_3=18 2x_1+3x_2-4x_3=-5 x_1-x_2+2x_3=9

Linear algebra

Simplify the Matrix

Given (x+5)/(x-1) if x<=-3 4x+9 if x>-3 ; what is 2(g(3))+g(-4) ?

Linear algebra

Simplify the Matrix

x>=0 : square root of 5x( square root of 8x^2-2 square root of x)

Linear algebra

Simplify the Matrix

p(x):|1+2x|=7 q(x):|x-3|=1-x

Linear algebra

Find the Square Roots of a Complex Number

5+2i

Linear algebra

Simplify the Matrix

(a^3b^-2)/(ab^-4) , a!=0 , b!=0

Linear algebra

Find the Cube Roots of a Complex Number

-4-4i

Linear algebra

Simplify the Matrix

(3a^2b^-4)/(12a^-2b^-2) , a!=0 , b!=0

Linear algebra

Solve using Gaussian Elimination

x+y+z=7 x-y+2z=7 2x+3z=14

Linear algebra

Solve using Gaussian Elimination

2x-4y=4 x-2y=2

Linear algebra

Simplify the Matrix

Find DE_ifD=[[-2,4,6],[5,-7,-1]] and E=[[1,-2],[0,4],[-3,4]]

Linear algebra

Solve using Gaussian Elimination

x+2y=5 2x+3y=6

Linear algebra

Simplify the Matrix

(3x^2)/(x^2-25)-x/(x+5)+2/(x-5) , x!=-5 , 5

Linear algebra

Find the Norm

[[3,6,0,9,8,7]]

Linear algebra

Find the Fourth Roots of a Complex Number

-3+4i

Linear algebra

Simplify the Matrix

(xy^-6)/(x^-4y^2) , x!=0 , y!=0

Linear algebra