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1 answer:
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<u>Answer:</u>
gradient = =
y-intercept =
<u>Step-by-step explanation:</u>
• The slope-intercept form of an equation takes the general form:
,
where:
m = slope,
c = y-intercept.
• We are given the equation:
To change this into the slope-intercept form, we must make y the subject:
[subtract
from both sides]
⇒ [divide both sides by 3]
⇒
• Comparing this equation with the general form equation, we see that:
m =
c = .
This means that the gradient is , and the y-intercept is
.
Answer:
Results are (1) True. (2) False. (3) False. (4) True. (5) True. (6) True.
Step-by-step explanation:
Given A is an matrix. Let
be the corresponding linear transformationover the field F and
be identity vector in V. Now if
.
(1) The kernel of a linear transformation is a vector space : True.
Let , then,
hence the kernel is closed under addition.
Let , then
and thus Ket(T) is closed under multiplication
Finally, fore all vectors ,
Thus Ker(T) is a subspace.
(2) If the equation Ax=b is consistent, then Col(A) is : False
if the equation Ax=b is consistent, then Col(A) must be consistent for all b.
(3) The null space of an mxn matrix is in
: False
The null space that is dimension of solution space of an m x n matrix is always in .
(4) The column space of A is the range of the mapping
: True.
(5) Col(A) is the set of all vectors that can be written as Ax for some x. : True.
Here Ax will give a linear combination of column of A as a weights of x.
(6) The null space of A is the solution set of the equation Ax=0.
: True