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amid [387]
3 years ago
12

If the null space of A4×5 is exactly a two-dimensional plane, answer the following:

Mathematics
1 answer:
Hatshy [7]3 years ago
8 0

Answer:

I.

A is a 4 x 5 matrix => A: U -> V, dim U = 5, dim V = 4

Null space is exactly two dimensional plane

dim null (A) = 2

II.

Rank A = dim U - dim Null A = 5 - 2 = 3

III.

Number of linearly Independent columns of A is the rank of A = 3

IV.

Yes, The system Ax = b has no solution sometimes as range of A \neq V

V.

Yes,Sometimes Ax = b has a unique solution

VI.

Yes, sometimes Ax = b has infinitely many solutions

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Answer:

x=-2 or x=3

Step-by-step explanation:

2(-2)+4=0

3-3=0

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3 years ago
Find the approximate length of the diagonal of the rectangle.
nevsk [136]

Answer:

Option A. 4.3\ cm

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we know that

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3 years ago
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3 years ago
25-29 please with work
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4 0
3 years ago
WILL GIVE BRAINLIEST
Amanda [17]

════════ ∘◦❁◦∘ ════════

<h3>Answer : y = ⅚x - 3</h3>

════════════════════

<h3>Known</h3>

x1 = 6

y1 = 2

x2 = (-6)

y2 = (-8)

════════════════════

<h3>Question</h3>

Equation of the line (y = mx + c)

════════════════════

<h3>Way to do</h3>

#First, you find the gradient (m)

m =  \frac{y2 - y1}{x2 - x1}  =  \frac{(( - 8) - 2)}{(( - 6) - 6)}  =  \frac{( - 10)}{( - 12)}  =  \frac{5}{6}

#Now use the formula of equation of the line

y - y1 = m(x - x1)

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════════════════════

3 0
3 years ago
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