Systems of equations and inequalities
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
|
|
||||
|---|---|---|---|---|---|
| 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)
🗑
|
Review the information in the table. When you are ready to quiz yourself you can hide individual columns or the entire table. Then you can click on the empty cells to reveal the answer. Try to recall what will be displayed before clicking the empty cell.
To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
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
Normal Size Small Size show me how
Created by:
drjolley
Popular Math sets