WorksheetsLinear Systems Matrices
Total questions: 25
Worksheet time: 31mins
What is the purpose of row operations in solving augmented matrices?
To create a new matrix
To find the determinant of the matrix
To calculate the inverse of the matrix
To simplify and solve the system of equations.
What are the three row operations used to solve augmented matrices?
Interchange two rows, Multiply a row by a non-zero constant, Add a multiple of one row to another row
Swap two rows
Divide a row by a non-zero constant
Subtract a multiple of one row from another row
What in the answer matrix indicates that there is an infinite number of solutions, infinitely many solutions?
the first part of the solution matrix will look like the identity matrix
The solution matrix will be a square matrix
One of the rows in the solution matrix will have all zeros
One of the rows in the solution matrix will have zeros and 1 number.
What in the answer matrix indicates that there is no solution?
the first part of the solution matrix will look like the identity matrix
The solution matrix will be a square matrix
One of the rows in the solution matrix will have all zeros
One of the rows in the solution matrix will have zeros and 1 number.
Reduced Row Echelon Form is where ______________________
Zeroes in the first column of my matrix
Thel ast column has all zeroes
One's are in a diagonal pattern of my matrix with zeroes underneath the one's.before the augmented portion
One's are in a diagonal pattern of my matrix with zeroes above and below the ones before the augmented portion
What is the difference between row echelon form and reduced row echelon form?
The row echelon form allows for leading coefficients other than 1.
The reduced row echelon form does not require the leading coefficient to be 1.
The difference between row echelon form and reduced row echelon form is that the reduced row echelon form has the additional condition that the leading coefficient of each nonzero row is always 1.
The row echelon form has more strict conditions for zero rows than the reduced row echelon form.
This is an example of
Row Echelon Form
Reduced Row Echelon Form
Really Reduced Echelon Form
Really Really Easy Form
This is an example of a
System of Quadratic Equations
Reduced Row Echelon Form
Augmented Matrix
A Canine Doing a Backflip
Solve, if possible.
x - y + 2z = -1
-3x + 3y + 5z = 3
2x - 2y = -2
x = 1, y = 1, z = 4
No solution
Infinitely many solutions
x = -1, y = -1, z = 4
Solve, if possible.
2x + 5y + z = -12
-x + 4y + 3z = -4
5x - 2z = -13
x = 3, y = 1, z = 1
No solution
Infinitely many solutions
x = -3, y = -1, z = -1
Solve, if possible.
3x + 3y = -12
-4x - 2y + 2z = -14
x + 3y + 2z = 11
x = 1, y = 1, z = 4
No solution
Infinitely many solutions
x = -1, y = -1, z = 4
Solve, if possible.
4x - 2y = 2
5x - 2y + z = 7
3x + 4y - z = 3
x = 1, y = 1, z = 4
No solution
Infinitely many solutions
x = -3, y = -1, z = -1
3x+5y-z=4
x-2y-3z=6
3x-5y-z=4
x+2y-3x=6
3x-5y+z=-4
x-2y-3z=6
3x-5y-z=4
x-2y-3z=-6
What is the solution to the 4x5 Matrix?
( 3, 4, 9, 6 )
( 3, 4, 9, -6 )
( -6, 9, 4, 3 )
( 6, 9, 4, 3 )
What is the solution to the systems of equations represented by the 3x4 Matrix?
(4, 6, 2)
(-6, 2, 2)
All Real Numbers
No Solutions
(2,3,5,0)
(2,3,4,5)
All Real Numbers
No Solution
Using back-substitution, calculate the solution for the REF matrix.
(3, -6, 3)
(-6, -6, 3)
(6, -6, 3)
(-6, -6, 3)
14.80x + 17y = 91
14.80x + 17y = 6
14.80y + 17x = 91
14.80x+ 17y = 6
Johnny was using Gaussian Elimination to simplify the matrix. What did he do wrong in this step?
To get a zero for a number you should multiply the same row by its' reciprocal
If you multiply a number to a row you have to change that row too
He added the numbers incorrectly
Nothing. This step was correct.
Jessica is simplifying the matrix using Gaussian Elimination. Did she complete the step correctly?
No, she should have changed the 2 to a zero and multiplied -2 by R2 and added R1
No, she wanted to change the 3 to a zero so she should have multiplied R2 and added it to R3
Yes. When you need a zero you multiply by the number's reciprocal.
No. Just punch in the calculator. Who cares about Carl Gauss
Please draw how you feel about Systems of Linear Equations on the big bird scale :)
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