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
Multiply the denominators with the numerators and write in one line, then solve for d.
The answer would be C, because 24+64 equals 88. And if you complete the expression 8(3+8), first solve the equation in the parentheses aka 8+3. Which gets you too 11. And now you multiply 8 by 11, and get 88 as your answer.
Answer:
125
Step-by-step explanation:
A full circle is 360°
80+85+70=235
360-235=125
Remember (a²-b²)=(a-b)(a+b)
solve for a single variable
solve for y in 2nd
add y to both sides
x²-7=y
sub (x²-7) for y in other equaiton
4x²+(x²-7)²-4(x²-7)-32=0
expand
4x²+x⁴-14x²+49-4x²+28-32=0
x⁴-14x²+45=0
factor
(x²-9)(x²-5)=0
(x-3)(x+3)(x-√5)(x+√5)=0
set each to zero
x-3=0
x=3
x+3=0
x=-3
x-√5=0
x=√5
x+√5=0
x=-√5
sub back to find y
(x²-7)=y
for x=3
9-7=2
(3,2)
for x=-3
9-7=2
(-3,2)
for √5
5-7=-2
(√5,-2)
for -√5
5-7=-2
(-√5,-2)
the intersection points are
(3,2)
(-3,2)
(√5,-2)
(-√5,-2)
