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سأعطيك صورة فيها اسإلة في mathématiques اعطني الأ...

Criado em: 8 de julho de 2025

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Pergunta

17519675312502964542058832359875.jpg17519675312502964542058832359875.jpg

سأعطيك صورة فيها اسإلة في mathématiques
اعطني الأجوبة بشكل مختصر
حلل الصورة جيدا و اعطني الاجوبة الصحيحة
اعطني الجواب فقط

Python

python
from PIL import Image
import matplotlib.pyplot as plt

img = Image.open('/mnt/data/17519675312502964542058832359875.jpg')
plt.imshow(img)
plt.axis('off')

(-0.5, 3999.5, 2999.5, -0.5)

Python

python
import numpy as np

# display half left region
w, h = img.size
left = img.crop((0,0,w//2,h))
plt.imshow(left)
plt.axis('off')

(-0.5, 1999.5, 2999.5, -0.5)

Python

python
# crop smaller region around q1
crop1 = img.crop((0, 500, 1400, 1800))  # adjust
plt.imshow(crop1)
plt.axis('off')

(-0.5, 1399.5, 1299.5, -0.5)

Python

python
# try crop q1 options region further down
crop1 = img.crop((0, 550, 1200, 1150))
plt.imshow(crop1)
plt.axis('off')

(-0.5, 1199.5, 599.5, -0.5)

Python

python
# crop region lower further
crop2 = img.crop((0, 1000, 1400, 2200))
plt.imshow(crop2)
plt.axis('off')

(-0.5, 1399.5, 1199.5, -0.5)

Python

python
crop3 = img.crop((0, 1800, 1400, 3000))
plt.imshow(crop3)
plt.axis('off')

(-0.5, 1399.5, 1199.5, -0.5)

Python

python
right = img.crop((1400, 0, w, h))
plt.imshow(right)
plt.axis('off')

(-0.5, 2599.5, 2999.5, -0.5)

Python

python
# crop for q3 (upper left of right half)
crop_q3 = img.crop((1200, 500, 2000, 1600))
plt.imshow(crop_q3)
plt.axis('off')

(-0.5, 799.5, 1099.5, -0.5)

Python

python
crop_q3_opts = img.crop((1200, 1500, 2000, 2600))
plt.imshow(crop_q3_opts)
plt.axis('off')

(-0.5, 799.5, 1099.5, -0.5)

Python

python
crop_q4 = img.crop((1200, 2500, 2000, 3500))
plt.imshow(crop_q4)
plt.axis('off')

(-0.5, 799.5, 999.5, -0.5)

Python

python
# crop q1 region fully
crop_q1 = img.crop((200, 800, 1100, 1800))
plt.imshow(crop_q1)
plt.axis('off')

(-0.5, 899.5, 999.5, -0.5)

Python

python
# crop the system bracket area right of q1
system1 = img.crop((950, 700, 1400, 1150))
plt.imshow(system1)
plt.axis('off')

(-0.5, 449.5, 449.5, -0.5)

Python

python
system1_bottom = img.crop((950, 1150, 1400, 1600))
plt.imshow(system1_bottom)
plt.axis('off')

(-0.5, 449.5, 449.5, -0.5)

Python

python
import sympy as sp
x,y,z = sp.symbols('x y z')
sol = sp.solve([x+2*y+z-2, 4*x+z-4, x+2*y+2*z-6], [x,y,z], dict=True)
sol

[{x: 0, y: -1, z: 4}]

Python

python
# crop system S2 for clarity
sys2 = img.crop((900, 1550, 1400, 2100))
plt.imshow(sys2)
plt.axis('off')

(-0.5, 499.5, 549.5, -0.5)

Python

python
opts2 = img.crop((200, 1600, 1100, 2800))
plt.imshow(opts2)
plt.axis('off')

(-0.5, 899.5, 1199.5, -0.5)

Python

python
plt.figure(figsize=(4,6))
plt.imshow(opts2)
plt.show()

Python

python
sol2_candidate = {x:-1/5, y:-3/5, z:1}
evaluations = [2*sol2_candidate[x]+sol2_candidate[y]+3*sol2_candidate[z], 5*sol2_candidate[x]+4*sol2_candidate[z], 3*sol2_candidate[x]-sol2_candidate[y]+sol2_candidate[z]]
evaluations

[2.0, 3.0, 0.9999999999999999]

Python

python
sol2 = sp.solve([2*x + y + 3*z - 2, 5*x + 4*z -3, 3*x - y + z -1], [x,y,z], dict=True)
sol2

[{x: 3/5 - 4*z/5, y: 4/5 - 7*z/5}]

Python

python
# enhance view with zoom
zoom = opts2.crop((0, 450, 400, 750))
plt.imshow(zoom)
plt.axis('off')

(-0.5, 399.5, 299.5, -0.5)

Python

python
zoom_top = opts2.crop((0, 200, 400, 400))
plt.imshow(zoom_top)
plt.axis('off')

(-0.5, 399.5, 199.5, -0.5)

Python

python
zoom_B = opts2.crop((0, 300, 400, 500))
plt.imshow(zoom_B)
plt.axis('off')

(-0.5, 399.5, 199.5, -0.5)

Python

python
zoom_param = opts2.crop((0, 500, 400, 900))
plt.imshow(zoom_param)
plt.axis('off')

(-0.5, 399.5, 399.5, -0.5)

Python

python
zoom_single = opts2.crop((0, 450, 400, 650))
plt.imshow(zoom_single)
plt.axis('off')

(-0.5, 399.5, 199.5, -0.5)

Python

python
zoom_param2 = opts2.crop((0, 650, 400, 950))
plt.imshow(zoom_param2)
plt.axis('off')

(-0.5, 399.5, 299.5, -0.5)

Python

python
import numpy as np
A = np.array([[1,0,2],[0,-1,1],[1,-2,0]])
B = np.array([[2,1,3],[5,0,4],[3,-1,1]])
np.dot(A,B)

array([[ 8, -1,  5],
       [-2, -1, -3],
       [-8,  1, -5]])

Python

python
# crop part listing product first candidate matrix
product_candidate = img.crop((1250, 1050, 1750, 1750))
plt.imshow(product_candidate)
plt.axis('off')

(-0.5, 499.5, 699.5, -0.5)

Python

python
letter_under_first = img.crop((1200, 1500, 1350, 1600))
plt.imshow(letter_under_first)
plt.axis('off')

(-0.5, 149.5, 99.5, -0.5)

Python

python
letter_A = img.crop((1200, 1400, 1300, 1450))
plt.imshow(letter_A)
plt.axis('off')

(-0.5, 99.5, 49.5, -0.5)

Python

python
# crop for Q5
crop_q5 = img.crop((1200, 2600, 2000, 3400))
plt.imshow(crop_q5)
plt.axis('off')

(-0.5, 799.5, 799.5, -0.5)

Python

python
# check full extent image size
print(img.size)

Python

python
crop_q5b = img.crop((1000, 2000, 2000, 2990))
plt.imshow(crop_q5b)
plt.axis('off')

(-0.5, 999.5, 989.5, -0.5)

Python

python
crop_q5c = img.crop((1000, 2400, 2000, 2990))
plt.imshow(crop_q5c)
plt.axis('off')

(-0.5, 999.5, 589.5, -0.5)

Python

python
crop_q5d = img.crop((1000, 2700, 2000, 3100))
plt.imshow(crop_q5d)
plt.axis('off')

(-0.5, 999.5, 399.5, -0.5)

Python

python
import sympy as sp
a,b,c = sp.symbols('a b c')
V1 = sp.Matrix([0,1,1])
V2 = sp.Matrix([1,0,1])
V3 = sp.Matrix([1,1,0])
w = sp.Matrix([1,2,3])
sol5 = sp.solve(V1*a + V2*b + V3*c - w, [a,b,c])
sol5

{a: 2, b: 1, c: 0}

Python

python
crop_q6 = img.crop((1600, 600, 2400, 1600))
plt.imshow(crop_q6)
plt.axis('off')

(-0.5, 799.5, 999.5, -0.5)

Python

python
crop_q6b = img.crop((2400, 600, 3400, 2000))
plt.imshow(crop_q6b)
plt.axis('off')

(-0.5, 999.5, 1399.5, -0.5)

Python

python
inv_option1 = img.crop((1600, 900, 2200, 1600))
plt.imshow(inv_option1)
plt.axis('off')

(-0.5, 599.5, 699.5, -0.5)

Python

python
options6 = img.crop((2050, 850, 2450, 1350))
plt.imshow(options6)
plt.axis('off')

(-0.5, 399.5, 499.5, -0.5)

Python

python
option6A = img.crop((2400, 900, 2800, 1450))
plt.imshow(option6A)
plt.axis('off')

(-0.5, 399.5, 549.5, -0.5)

Python

python
option6C = img.crop((2400, 1400, 3000, 2200))
plt.imshow(option6C)
plt.axis('off')

(-0.5, 599.5, 799.5, -0.5)

Python

python
A = sp.Matrix([[1,0,2],[0,-1,1],[1,-2,0]])
A.det()

4

Python

python
A_inv = A.inv()
A_inv

Matrix([
[1/2,   -1,  1/2],
[1/4, -1/2, -1/4],
[1/4,  1/2, -1/4]])

Python

python
# zoom area between first and second inverse to see letter B or something
option6_letterC = img.crop((2200, 1200, 2300, 1350))
plt.imshow(option6_letterC)
plt.axis('off')

(-0.5, 99.5, 149.5, -0.5)

Python

python
q7 = img.crop((1700, 2000, 2700, 2800))
plt.imshow(q7)
plt.axis('off')

(-0.5, 999.5, 799.5, -0.5)

Python

python
q7stmt = img.crop((1300, 1900, 2300, 2150))
plt.imshow(q7stmt)
plt.axis('off')

(-0.5, 999.5, 249.5, -0.5)

Python

python
q7stmt2 = img.crop((2300, 1900, 2600, 2300))
plt.imshow(q7stmt2)
plt.axis('off')

(-0.5, 299.5, 399.5, -0.5)

Python

python
B = sp.Matrix([[2,1,3],[5,0,4],[3,-1,1]])
B.rank()

2

Python

python
q8 = img.crop((1700, 2700, 2500, 3200))
plt.imshow(q8)
plt.axis('off')

(-0.5, 799.5, 499.5, -0.5)

Python

python
# compute 5A - 2B
result9 = 5*A - 2*B
result9

Matrix([
[  1, -2,  4],
[-10, -5, -3],
[ -1, -8, -2]])

Python

python
q9 = img.crop((2700, 600, 3600, 2000))
plt.imshow(q9)
plt.axis('off')

(-0.5, 899.5, 1399.5, -0.5)

Python

python
q10 = img.crop((2700, 2000, 3800, 3000))
plt.imshow(q10)
plt.axis('off')

(-0.5, 1099.5, 999.5, -0.5)

Python

python
q10map = img.crop((2600, 1950, 3300, 2150))
plt.imshow(q10map)
plt.axis('off')

(-0.5, 699.5, 199.5, -0.5)

Python

python
q10map2 = img.crop((2900, 2170, 3600, 2350))
plt.imshow(q10map2)
plt.axis('off')

(-0.5, 699.5, 179.5, -0.5)

Python

python
q10map3 = img.crop((2900, 2350, 3600, 2600))
plt.imshow(q10map3)
plt.axis('off')

(-0.5, 699.5, 249.5, -0.5)

Python

python
snippet_q7map = img.crop((2250, 2150, 2850, 2350))
plt.imshow(snippet_q7map)
plt.axis('off')

(-0.5, 599.5, 199.5, -0.5)

Python

python
q10mathexpr = img.crop((2950, 2050, 3250, 2200))
plt.imshow(q10mathexpr)
plt.axis('off')

(-0.5, 299.5, 149.5, -0.5)

Python

python
q10map4 = img.crop((3050, 2050, 3700, 2250))
plt.imshow(q10map4)
plt.axis('off')

(-0.5, 649.5, 199.5, -0.5)

Python

python
# crop specific area text again with larger resolution maybe
q10vec = img.crop((3100, 2380, 3500, 2500))
plt.imshow(q10vec)
plt.axis('off')

(-0.5, 399.5, 119.5, -0.5)

Python

python
q10vec2 = img.crop((3350, 2340, 3950, 2550))
plt.imshow(q10vec2)
plt.axis('off')

(-0.5, 599.5, 209.5, -0.5)

Pensamento

For the vector (1,-1,-1/2), it would fit if the mapping was x - 2y (with a negative y coefficient). But testing it with the mapping, I see that it doesn't work—there’s a mismatch in the result. The vector doesn’t belong in the kernel. So I’ve decided to stick with (1,-1,1/2). Option E uses the wrong sign, and the cropping in Q10 might be affecting the final result—last entry could be ‘1’ instead of ‘-1’. I'll adjust the crop to get a clearer view.

Thought for 12m 9s

Resposta

  1. B
  2. D
  3. A
  4. A
  5. B
  6. A
  7. B
  8. A
  9. E
  10. C

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