Error installing tensorflow gpu ubuntu

Hello, I am following the official guide on how to install Tensorflow using pip.
First I have detected what kind of GPU I am using on my Ubuntu 20 machine

$ lspci | grep VGA
01:00.0 VGA compatible controller: NVIDIA Corporation GK107 [GeForce GT 640 OEM] (rev a1)

Then I downloaded the NVIDIA drivers from the official page, I have selected the one for the GeForce 600 series, specifically the 470.141.03 version.
The process of installing conda and creating a new environment went smoothly and also while installing tensorflow through pip I did not encounter any kind of error.
Unfortunately now that I am verifying if everything works correctly I get the following error

$ python3 -c "import tensorflow as tf; print(tf.reduce_sum(tf.random.normal([1000, 1000])))"

2022-09-29 14:11:23.467663: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcudart.so.11.0'; dlerror: libcudart.so.11.0: cannot open shared object file: No such file or directory
2022-09-29 14:11:23.467704: I tensorflow/stream_executor/cuda/cudart_stub.cc:29] Ignore above cudart dlerror if you do not have a GPU set up on your machine.
2022-09-29 14:11:23.520203: E tensorflow/stream_executor/cuda/cuda_blas.cc:2981] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
2022-09-29 14:11:24.852647: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer.so.7'; dlerror: libnvinfer.so.7: cannot open shared object file: No such file or directory
2022-09-29 14:11:24.852760: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer_plugin.so.7'; dlerror: libnvinfer_plugin.so.7: cannot open shared object file: No such file or directory
2022-09-29 14:11:24.852779: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Cannot dlopen some TensorRT libraries. If you would like to use Nvidia GPU with TensorRT, please make sure the missing libraries mentioned above are installed properly.
2022-09-29 14:11:25.664198: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:980] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2022-09-29 14:11:25.664624: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcudart.so.11.0'; dlerror: libcudart.so.11.0: cannot open shared object file: No such file or directory
2022-09-29 14:11:25.664706: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcublas.so.11'; dlerror: libcublas.so.11: cannot open shared object file: No such file or directory
2022-09-29 14:11:25.664791: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcublasLt.so.11'; dlerror: libcublasLt.so.11: cannot open shared object file: No such file or directory
2022-09-29 14:11:25.664867: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcufft.so.10'; dlerror: libcufft.so.10: cannot open shared object file: No such file or directory
2022-09-29 14:11:25.664994: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcurand.so.10'; dlerror: libcurand.so.10: cannot open shared object file: No such file or directory
2022-09-29 14:11:25.665069: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcusolver.so.11'; dlerror: libcusolver.so.11: cannot open shared object file: No such file or directory
2022-09-29 14:11:25.665151: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcusparse.so.11'; dlerror: libcusparse.so.11: cannot open shared object file: No such file or directory
2022-09-29 14:11:25.665216: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcudnn.so.8'; dlerror: libcudnn.so.8: cannot open shared object file: No such file or directory
2022-09-29 14:11:25.665229: W tensorflow/core/common_runtime/gpu/gpu_device.cc:1934] Cannot dlopen some GPU libraries. Please make sure the missing libraries mentioned above are installed properly if you would like to use GPU. Follow the guide at https://www.tensorflow.org/install/gpu for how to download and setup the required libraries for your platform.
Skipping registering GPU devices...
tf.Tensor(215.02896, shape=(), dtype=float32)

This also happens if I try to verify the GPU setup. I didn’t find a solution on the wiki, does anyone know how to fix this?

Have you followed the tested build configurations? Thank you.

I was looking at the various combinations and I have a doubt, is there a way to find which version of cuda and cudnn are supported by my GPU?

Looking at the hardware requirements it seems that the GPU must be compatible with Cuda 3.5 or higher.
This seems to be incompatible with my GPU looking at this guide. I think that for this reason is not possible to make tensorflow-gpu work on my computer.
I would still like to know if Tensorflow with only CPU compatibility can be successfully installed.

I would still like to know if Tensorflow with only CPU compatibility can be successfully installed.

Yes, Tensorflow was installed successfully hence it returns tf.Tensor(215.02896, shape=(), dtype=float32) . Thank you.