Math 205 Latest Update 2024-2025 Questions and 100% Verified Correct Answers Guaranteed A+
consistent system of equations - CORRRECT ANSWER: has at least one solution
difference between minor and cofactor - CORRRECT ANSWER: minor is the resulting
matrix when you block the row and column, the cofactor is that but includes the (- 1)^m+n
differential equation - CORRRECT ANSWER: involves one or more derivatives of
unknown function y(t)
Gaussian elimination - CORRRECT ANSWER: reducing augmented matrix to row-
echelon form and using back substitution to solve the equivalent system
how to tell if inverse exists - CORRRECT ANSWER: If Ax=b has a unique solution,
rank(A)=n, then inverse exists.If homogeneous linear system Ax=0 has only trivial solution x=0, inverse exists.
how to tell if matrix is invertible - CORRRECT ANSWER: determinant cannot equal 0
If Ax=b is an nxn invertible matrix, then it has a unique solution, which is given by... -
CORRRECT ANSWER: x = (A^-1)(b)
inconsistent system of equations - CORRRECT ANSWER: has no solution
linear differential equation - CORRRECT ANSWER: components are functions of x only
order of differential equation - CORRRECT ANSWER: order of highest occurring
derivative
rank - CORRRECT ANSWER: number of nonzero rows in any row-echelon form of a
matrix
reduced row-echelon matrix - CORRRECT ANSWER: an column that contains a
leading 1 has zeros everywhere else
row-echelon matrix - CORRRECT ANSWER: 1. any rows consisting of all zeros are
grouped at bottom of matrix
- first non-zero element in any row must be a 1
- leading 1 of any row must be to the right of any leading 1 above it (diagonal)
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solution to a system - CORRRECT ANSWER: ordered scalars (c1,c2,c3,..) that can be substituted for the x's that yield the values on the right-hand side
steps to find the determinant - CORRRECT ANSWER: if matrix is greater than 3x3, first try using elementary row operations to get a row or column of zeros to expand about.Then find determinant using minors and co-factors.
steps to solve population growth or radioactive decay - CORRRECT ANSWER: usually initial values will be given which can be used to solve for constant in equation Q(t) = Q.e^(kt)
two ways to find the inverse - CORRRECT ANSWER: 1. use Gaussian elimination
augmented with identity matrix
- adjoint method
why do we care more about solving homogeneous linear differential equations? -
CORRRECT ANSWER: Whenever you solve a non homogeneous linear differential
equation, you end up first solving the associated homogeneous equation anyways.Capri said, "8,7,6,5" while putting up 4 fingers one at a time. The she said, "4 donuts." Is
Capri using direct modeling or a counting strategy? - CORRRECT ANSWER: Counting
strategy
Compare Difference Unknown Problem Type - CORRRECT ANSWER: Connie has 13
marbles. Juan has 5 marbles. How many more marbles does Connie have than Juan?
Compare Quantity Unknown Problem Type - CORRRECT ANSWER: Juan has 5
marbles. Connie has 8 more than Juan. How many marbles does Connie have?
Compare Referent Unknown Problem Type - CORRRECT ANSWER: Connie has 13
marbles. she has 5 ore marbles than Juan. How many marbles does Juan have?
Conceptual Subitizing - CORRRECT ANSWER: Is when we can instantly, or very
quickly, recognize how many objects there are because we recognize a familiar pattern, such as an array on a dice, or a 3x3 square.
Connie had 5 marbles. Juan gave her 8 more marbles. How many marbles does Connie have altogether?
What problem type is this? - CORRRECT ANSWER: Join Result Unknown
Connie had 13 marbles. She gave 5 to Juan. How many marbles does Connie have
left? - CORRRECT ANSWER: Separate Result Unknown
Connie had 13 marbles. She gave some to Juan. Now she has 5 marbles left. How
many marbles did Connie give to Juan? - CORRRECT ANSWER: Separate Change
Unknown
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