Busy. Please wait.
or

show password
Forgot Password?

Don't have an account?  Sign up 
or

Username is available taken
show password

why

Make sure to remember your password. If you forget it there is no way for StudyStack to send you a reset link. You would need to create a new account.

By signing up, I agree to StudyStack's Terms of Service and Privacy Policy.


Already a StudyStack user? Log In

Reset Password
Enter the associated with your account, and we'll email you a link to reset your password.

Remove ads
Don't know
Know
remaining cards
Save
0:01
To flip the current card, click it or press the Spacebar key.  To move the current card to one of the three colored boxes, click on the box.  You may also press the UP ARROW key to move the card to the "Know" box, the DOWN ARROW key to move the card to the "Don't know" box, or the RIGHT ARROW key to move the card to the Remaining box.  You may also click on the card displayed in any of the three boxes to bring that card back to the center.

Pass complete!

"Know" box contains:
Time elapsed:
Retries:
restart all cards




share
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

  Normal Size     Small Size show me how

Math1050 CH08

Systems of equations and inequalities

Side 1Side 2
A ___ of a system consists of all values for variables that are solutions to each equation in the system. solution
If a system has at least one solution, it is said to be ___. consistent
If a system has no solution it is said to be ___. inconsistent
A system of linear equations has lines that are either ___, ___, or ___. parallel, intersect, are coincident (the same line)
If the lines of a system of linear equations has one solution (intersection), the system is ___ and the equations are ___. consistent, independent
If the lines of a system of linear equations are ___ the system has no solution and the equations are ___. parallel, inconsistent
If the lines of a system of linear equations are coincident, the system has ___ solutions. The system is ___ and the equations are ___. infinite, consistent, dependent
In a matrix the first column represents the variable ___, the 2nd ___, and the 3rd ___. x, y, z
The matrix used to represent a system of equations is called ___. an augmented matrix
If a matrix doesn't include the numbers to the right of the = it is called ___. the coefficient matrix
___ are used to manipulate a matrix. Row operations
List the types of row operations of a matrix. 1. interchange any two rows. 2. replace a row by a NONZERO multiple of THAT row. 3. replace a row by the sum of that row and a constant NONZERO multiple of another row.
A matrix with the number one in diagonal from top left to bottom right with all entries below the '1s' being zero is called ___. row echelon form
A matrix with the number one in diagonal from top left to bottom right with ALL other entries being zero is called ___. reduced row echelon form
Using determinants to solve a system only works when ___. the number of equations equals the number of variables
Cramer's rule states that if D does not equal 0, x = ___, and y = ___. D_x/D, D_y/D
If D = 0, the system is either ___ or ___. inconsistent, has infinite solutions
When finding the determinant of a 3x3 matrix, three 2x2 determinants are formed called ___. minor determinants
For a square determinant, each determinant is multiplied by -1 raised to an exponent. This is called a ___. cofactor
The cofactor is found by ___. multiplying -1 by an exponent found by adding the number of the row and column together (row 1, column 2 would be 1+2=3. So raised to the third power.)
The cofactors of the first row of a 3x3 matrix are ___, ___, and ___. (-1)^2 or 1, (-1)^3 or -1, (-1)^4 or 1
The cofactors of the second row of a 3x3 matrix are ___, ___, and ___. (-1)^3 or -1, (-1)^4 or 1, (-1)^5 or -1
The cofactors of the third row of a 3x3 matrix are ___, ___, and ___. (-1)^4 or 1, (-1)^5 or -1, (-1)^6 or 1
T or F? You can use any row or column to find D. True. It's best to use one with a 0 to reduce work.
If D = 0 and at least one of the determinants is different from 0, then the system is ___ and the solution set is ___. inconsistent, { }
If D = 0 and all determinants are also 0, then the system is ___, the equations are ___, and the solution set is ___. consistent, dependent, all real numbers
The value of a determinant changes sign if any 2 rows (or columns) are ___. interchanged
If all entries in any row or column equal 0, the value of the determinant is ___. 0
If any 2 rows (or columns) of a determinant have corresponding entries that are equal, the value of the determinant is ___. 0
If any row (or column) of a determinant is multiplied by a nonzero number k, the value of the determinant is ___. also changed by a factor of k
If the entries of any row (or column) of a determinant are multiplied by a nonzero number k and the result is added to the corresponding entries of another row (or column), the value for the determinant ___. is unchanged
The sum or difference of 2 matrices is found by ___. adding or subtracting the corresponding entries of each to a new matrix
T or F? A 2x3 matrix and a 2x4 matrix can be added. F
T or F? The commutative property applies to addition of matrices. T
T or F? The associative property applies to addition of matrices. T
A ___ is a number that a matrix is multiplied by. scalar
A scalar multiple of a matrix is formed by ___. multiplying each entry by a scalar
k(hA) = (kh)A demonstrates the ___ property of scalar multiplication. associative
(k + h)A = kA + Ah demonstrates the ___ property of scalar multiplication. distributive
k(A + B) = kA + kB demonstrates the ___ property of scalar multiplication. distributive
A row vector R multiplied by a column vector C is defined as ___. r_1c_1 + r_2c_2 + r_3c_3...
A row vector and column vector can only be multiplied if they ___. have the same number of entries
When multiplying matrices, each entry of the product is found by ___. multiplying the corresponding row vector of the first matrix and the column vector of the second and adding together all of the products
T or F? For matrices, AB=BA. False
An identity matrix (I) is ___. A matrix with the number one in diagonal from top left to bottom right with ALL other entries being zero
Identity property, IA = ___. A
Identity property, AI = ___. A
(A^-1)A = ___. I
A(A^-1) = ___. I
T or F? Every matrix has an inverse. F
T or F? Every square matrix has an inverse. F
If a matrix has an inverse it is said to be ___ and ___ when it does not have an inverse. nonsingular, singular
What is the procedure for finding the inverse of a matrix? 1. form the matrix [A|I] 2. transform into reduced row echelon form 3. the matrix on the right is A^-1
The procedure of reducing rational expressions into the sum of simpler fractions is called ___. partial fraction decomposition
In partial fraction decomposition, the simpler fractions are called ___. partial fractions
Partial fraction decomposition only works with ___ fractions. proper
For improper fractions, ___ is used to reduce them. division
For the complex fraction P/Q, if Q has only nonrepeating linear factors, the partial fraction decomposition is of the form ___. A/(x-a) + B/(x-b)...
For the complex fraction P/Q, if Q has repeating linear factors, the partial fraction decomposition is of the form ___. A/(x-a) + B/(x-a)^2 + C/(x-a)^3...
For the complex fraction P/Q, if Q has nonrepeating irreducible quadratic factors, the partial fraction decomposition is of the form ___. ((Ax + B)/(ax^2 + bx + c))
For the complex fraction P/Q, if Q has repeating irreducible quadratic factors, the partial fraction decomposition is of the form ___. ((Ax + B)/(ax^2 + bx + c)) + ((Cx + D)/(ax^2 + bx + c)^2) + ((Ex + F)/(ax^2 + bx + c)^3)
Created by: drjolley