PLEASE HELP I HAVE ALOT OF QUESTIONS I WILL GIVE 25 POINTS!!!!!!
2 answers:
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There are 3 terms in this expression. You can determine this answer by knowing that terms are either a single number or variable or numbers and variables multiplied together. Here's a picture example below:
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Hope it helps! Mark as brainliest!
Answer:
True
True
False
Step-by-step explanation:
TRUE
If the equation Ax = 0 has only the trivial solution, then A is row equivalent to the n × n identity matrix
Here's why
If the equation Ax = 0 has only the trivial solution the determinant of the matrix is NOT 0 and the matrix is invertible therefore it is row equivalent to the nxn identity matrix.
TRUE
If the columns of A span ℝ^n , then the columns are linearly independent
Here's why
Remember that the rank nullity theorem states that
According to the information given we know that
Therefore you have
and
Which is equivalent to the problem we just solved.
FALSE
If A is an n × n matrix, then the equation Ax = b has at least one solution for each b in ℝ^n
Here's why
Take b as a non null vector and A=0, then Ax = 0 and Ax=b will have no solution.