ax=b solving with numpy llinalg gives "Last 2 dimensions of the array must be square" - numpy

Question

I have 3 matrices of shape (157, 4) , (157,) and (4,) respectively. The first matrix (an_array) contains the quantity of the items. the second, (Items matrix) contains the items names and the 3rd (Price matrix) one contains the price. I am trying to workout the price of individual items but I get an error saying "Last 2 dimensions of the array must be square" everytime I am trying to do
X = np.linalg.solve(an_array,price)
I am trying to solve ax=b but unfortunately its not working out. Any help would be very much appreciated.
**Price matrix**
array([499.25, 381. , 59.5 , 290. , 128.5 , 305.25, 336.25, 268.5 ,
395.25, 136.5 , 194.5 , 498.75, 62.25, 312.75, 332. , 171. ,
402.5 , 144.5 , 261.5 , 242.75, 381. , 371. , 355.5 , 373. ,
65.5 , 228.75, 208.75, 204.5 , 86.5 , 143. , 70.5 , 36.5 ,
82. , 302.5 , 365.5 , 158.5 , 316.5 , 508. , 86.5 , 359.75,
25.5 , 345.5 , 304.5 , 491.25, 181.5 , 343.75, 383.5 , 283.5 ,
140.25, 426. , 386. , 337.25, 415.5 , 268.25, 406. , 149.5 ,
200. , 122. , 510.25, 280. , 406.75, 191.25, 198. , 114.5 ,
211.5 , 241.75, 195.75, 276.25, 276. , 165.25, 102. , 425. ,
195. , 132.25, 86.75, 446.5 , 318. , 290.75, 286. , 232. ,
520.5 , 382.75, 94. , 482.75, 233.25, 262. , 368.25, 438.75,
433.5 , 334.5 , 360. , 422. , 191. , 292.25, 151.75, 440.25,
370. , 105.25, 122. , 455.5 , 363. , 436. , 147.5 , 548.5 ,
365.75, 185.5 , 348. , 342.5 , 509.25, 465.5 , 380.25, 361. ,
271.25, 414.25, 366.75, 145.5 , 348. , 471.25, 254.5 , 329. ,
441. , 253.25, 448.5 , 142. , 312.5 , 350. , 94. , 333. ,
418. , 194.5 , 543. , 212.5 , 66.5 , 370. , 423. , 164. ,
393.25, 299.75, 529.5 , 166.25, 228.5 , 476. , 373. , 383.25,
409. , 241. , 107.75, 194.5 , 350. , 221.75, 633.25, 444.25,
155.25, 76. , 542. , 346. , 159.75])
**Item matrix**
array(['Cereal', 'Coffee', 'Eggs', 'Pancake'], dtype='<U7')
#an_array matrix
array([[ 7, 6, 6, 9],
[ 6, 7, 0, 10],
[ 0, 7, 1, 0],
[ 4, 0, 10, 0],
[ 0, 0, 4, 2],
[10, 7, 0, 3],
[ 9, 1, 4, 3],
[ 9, 8, 0, 2],
[10, 0, 4, 5],
[ 6, 3, 0, 0],
[ 0, 1, 9, 0],
[ 3, 9, 9, 9],
[ 2, 0, 0, 1],
[ 6, 0, 6, 3],
[ 9, 0, 3, 4],
[ 8, 2, 0, 0],
[ 9, 0, 0, 10],
[ 5, 0, 0, 2],
[ 8, 7, 3, 0],
[ 0, 1, 6, 5],
[ 7, 0, 3, 8],
[ 0, 5, 10, 6],
[ 7, 1, 10, 0],
[ 4, 7, 10, 2],
[ 0, 0, 1, 2],
[ 2, 6, 0, 7],
[ 6, 4, 0, 3],
[ 8, 0, 0, 2],
[ 0, 0, 2, 2],
[ 3, 7, 0, 2],
[ 0, 9, 1, 0],
[ 1, 3, 0, 0],
[ 3, 4, 0, 0],
[ 4, 0, 0, 10],
[ 4, 9, 7, 4],
[ 6, 7, 0, 0],
[ 6, 9, 7, 0],
[ 6, 0, 10, 8],
[ 0, 0, 2, 2],
[ 6, 0, 4, 7],
[ 1, 1, 0, 0],
[ 3, 9, 7, 4],
[ 0, 1, 10, 4],
[ 6, 1, 10, 7],
[ 0, 2, 6, 2],
[ 4, 1, 7, 5],
[ 0, 3, 9, 8],
[ 3, 2, 8, 2],
[ 0, 10, 3, 1],
[ 4, 0, 8, 8],
[ 2, 0, 8, 8],
[ 7, 8, 2, 5],
[ 7, 2, 2, 10],
[ 0, 9, 3, 7],
[ 4, 4, 6, 8],
[ 5, 9, 0, 0],
[ 0, 2, 9, 0],
[ 4, 0, 2, 0],
[10, 9, 5, 7],
[ 4, 4, 0, 8],
[ 9, 10, 5, 3],
[ 4, 0, 0, 5],
[ 1, 0, 0, 8],
[ 1, 1, 0, 4],
[ 4, 1, 6, 0],
[ 0, 8, 2, 7],
[ 1, 5, 6, 1],
[ 4, 4, 3, 5],
[ 9, 6, 3, 0],
[ 2, 3, 2, 3],
[ 4, 4, 0, 0],
[ 8, 10, 10, 0],
[ 6, 6, 2, 0],
[ 0, 0, 1, 5],
[ 1, 0, 0, 3],
[ 7, 0, 4, 10],
[ 4, 8, 5, 4],
[ 9, 8, 0, 3],
[ 4, 6, 4, 4],
[10, 2, 1, 0],
[10, 3, 6, 8],
[ 6, 8, 3, 7],
[ 0, 9, 0, 2],
[ 8, 7, 4, 9],
[ 0, 6, 0, 9],
[ 0, 0, 4, 8],
[ 0, 0, 8, 9],
[ 8, 8, 8, 3],
[ 3, 5, 8, 8],
[ 7, 3, 0, 8],
[ 9, 6, 7, 0],
[ 8, 0, 4, 8],
[ 9, 2, 0, 0],
[ 6, 3, 0, 7],
[ 0, 4, 3, 3],
[10, 1, 8, 3],
[ 5, 10, 6, 4],
[ 0, 7, 0, 3],
[ 4, 0, 2, 0],
[10, 6, 0, 10],
[ 4, 0, 5, 8],
[10, 0, 7, 4],
[ 1, 7, 0, 4],
[10, 0, 6, 10],
[ 8, 10, 4, 3],
[ 9, 1, 0, 0],
[ 9, 0, 8, 0],
[ 6, 0, 0, 10],
[ 9, 1, 8, 7],
[ 1, 10, 8, 10],
[ 0, 6, 7, 9],
[10, 5, 0, 6],
[ 0, 10, 5, 5],
[ 8, 6, 1, 9],
[ 0, 4, 9, 7],
[ 4, 0, 1, 2],
[ 3, 9, 5, 6],
[10, 10, 5, 5],
[ 5, 0, 1, 6],
[ 9, 8, 5, 0],
[ 8, 3, 2, 10],
[ 0, 2, 2, 9],
[ 5, 9, 10, 4],
[ 6, 4, 0, 0],
[ 8, 1, 7, 0],
[ 6, 7, 7, 2],
[ 0, 9, 0, 2],
[10, 8, 0, 4],
[10, 1, 8, 2],
[ 0, 3, 0, 8],
[10, 8, 10, 4],
[ 0, 0, 8, 2],
[ 0, 4, 0, 2],
[ 8, 0, 10, 0],
[ 7, 0, 5, 8],
[ 6, 8, 0, 0],
[ 8, 6, 0, 9],
[10, 6, 0, 3],
[ 9, 4, 5, 10],
[ 0, 10, 0, 5],
[ 6, 4, 2, 2],
[ 9, 10, 3, 8],
[ 8, 3, 3, 6],
[ 6, 0, 3, 9],
[ 3, 1, 10, 6],
[ 0, 0, 3, 8],
[ 4, 1, 0, 1],
[ 5, 1, 0, 4],
[ 7, 0, 10, 0],
[ 5, 10, 0, 3],
[10, 8, 9, 9],
[10, 6, 9, 1],
[ 0, 8, 0, 5],
[ 0, 10, 1, 0],
[ 8, 7, 10, 6],
[ 0, 0, 8, 8],
[ 0, 5, 1, 5]])

Answer 1

you have 4 variables that are present in 157 equations, and you need to solve for the 4 variables, this system has no solution and is not solved by a linear system solution, rather as a least squares solution using np.linalg.lstsq
X = np.linalg.lstsq(an_array, price)[0]
print(X)

Answer 2

Using the lstsqr as recommended by #Ahmed:
In [88]: X = np.linalg.lstsq(quant, price)[0]
C:\Users\paul\AppData\Local\Temp\ipykernel_6428\995094510.py:1: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.
To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.
X = np.linalg.lstsq(quant, price)[0]
In [90]: X
Out[90]: array([20. , 5.5 , 21. , 22.25])
Multiplying the quantities by these prices and summing gives the same numbers as your price array:
In [91]: quant#X
Out[91]:
array([499.25, 381. , 59.5 , 290. , 128.5 , 305.25, 336.25, 268.5 ,
395.25, 136.5 , 194.5 , 498.75, 62.25, 312.75, 332. , 171. ,
... , 159.75])
So there's no noise in these prices - the values are exact. That means you could use solve with any 4 of the price and quant values. That addresses the "must be square" error. quant[:4,:] has (4,4) shape.
In [92]: np.linalg.solve(quant[:4,:], price[:4])
Out[92]: array([20. , 5.5 , 21. , 22.25])