Which terms could be used as the last term of the expression below to create a polynomial written in standard form? Check all th
2 answers:
A polynomial is said to be in standard form if it is written in the order of degree from highest to lowest from left to right.
The degree of a term of a polynomial is the exponent of the variable or the sum of the exponents of the variables of that term of the polynomial.
Thus, given the expression
has a degree of 6, and
has a degree of 6.
Thus, the exponent of the variable or the sum of the exponents of the variables of the next term of the polynomial must be less than or equal to 6 for the polynomal to be said to be in standars form.
Therefore, the <span>terms that could be used as the last term of the given expression to create a polynomial written in standard form are
</span>
The degree of a term of a polynomial is the exponent of the variable or the sum of the exponents of the variables of that term of the polynomial.
Thus, given the expression
Thus, the exponent of the variable or the sum of the exponents of the variables of the next term of the polynomial must be less than or equal to 6 for the polynomal to be said to be in standars form.
Therefore, the <span>terms that could be used as the last term of the given expression to create a polynomial written in standard form are
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Answer:
C. True; by the Invertible Matrix Theorem if the equation Ax=0 has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the n x n identity matrix.
Step-by-step explanation:
The Invertible matrix Theorem is a Theorem which gives a list of equivalent conditions for an n X n matrix to have an inverse. For the sake of this question, we would look at only the conditions needed to answer the question.
- There is an n×n matrix C such that CA=
.
- There is an n×n matrix D such that AD=
- The equation Ax=0 has only the trivial solution x=0.
- A is row-equivalent to the n×n identity matrix
- For each column vector b in
, the equation Ax=b has a unique solution.
- The columns of A span
Therefore the statement:
If there is an n X n matrix D such that AD=I, then there is also an n X n matrix C such that CA = I is true by the conditions for invertibility of matrix:
- The equation Ax=0 has only the trivial solution x=0.
- A is row-equivalent to the n×n identity matrix
The correct option is C.