How to see if matrix is one to one calculator
Answers
Answer:
look at the pivots (the leading 1's of the rows)
Step-by-step explanation:
Then, look at the pivots (the leading 1's of the rows). If we have a pivot in every column, then the nullspace of the matrix (and hence the kernel of T) is zero-dimensional. So, T is one-to-one if and only if the REF has pivot in every column.
Final answer:
To check if a matrix is one-to-one using a calculator, you need to enter the matrix values into the calculator, find the reduced row echelon form (RREF) of the matrix, and if the RREF is the identity matrix, the matrix is one-to-one.
Explanation:
In Linear Algebra, a matrix is considered one-to-one if each input vector from a given set of vectors gives a unique output vector. In other words, no two different input vectors can yield the same output vector. To check whether a matrix is one-to-one using a calculator, you’re essentially checking if the transformation represented by the matrix is injective. Here are the steps:
- Enter the values of your matrix into the calculator.
- Find the reduced row echelon form (RREF) of the matrix. You can do this by row reducing the matrix.
- If the RREF of the matrix is the identity matrix, then the matrix is one-to-one. This means that every column of the matrix will have a leading 1, with zeros everywhere else in that column and row.
Note: These steps can often be performed on a calculator that has capabilities for matrix operations, like a TI-83 or TI-84.
Learn more about Matrix here:
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Answers
4y + 8 = 6y + 3
4y - 6y = 3 - 8
-2y = -5
-y = -5/2
-y = -2,5
y = 2.5
And if you use y back in the original equation, it will be:
4*2.5 + 8 = 6*2.5 +3
10 + 8 = 15 + 3
18 = 18
Answers
I’m really struggling
Answers
Answer:
(y - 1) = 4(x +1)
Step-by-step explanation:
slope = 4
B = -4
given point (-1,1)
y = 4x -4 (this is the slope intercept form)
(point slope form)
(y - 1) = 4(x +1) ... that is the point slope form
Answers
Answer:
Sarah has $18, and Lance has $42.
Step-by-step explanation:
We know that Sarah and Lance together have $60, so we can write the equation:
S + L = 60
We also know that Lance has six more than twice as much as Sarah, which can be expressed as:
L = 2S + 6
Now, we have a system of two equations:
S + L = 60
L = 2S + 6
We can use substitution or elimination to solve this system. Let's use substitution:
From equation 2, we can express L in terms of S:
L = 2S + 6
Now, substitute this expression for L into equation 1:
S + (2S + 6) = 60
Combine like terms:
3S + 6 = 60
Subtract 6 from both sides:
3S = 60 - 6
3S = 54
Now, divide by 3:
S = 54 / 3
S = 18
So, Sarah has $18.
Now, we can find Lance's amount using equation 2:
L = 2S + 6
L = 2(18) + 6
L = 36 + 6
L = 42
Lance has $42.
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Answer:
1) Linear Pair
2) Adjacent
3) Complmentary
4) Vertical
Answers
Volume = s³
s³ = 8000 in³
So, s = ³√8000 = 20 in