Serializing scriptableobjects array for savegame

I'm having trouble serializing an array of scriptableobjects (each is a sprite and a string).

I'm very new to serialization and I started building a serializer class based on the one in the tutorial.

Running this code:

 using UnityEngine;
 using System.Collections;
 
 using System.IO;
 using System.Runtime.Serialization.Formatters.Binary;
 using System;
 
 public class SaveManager : MonoBehaviour {
     public void Save()
     {
         BinaryFormatter bf = new BinaryFormatter ();
         FileStream file = File.Create (Application.persistentDataPath + "/playerInfo.dat");
         SaveData data = new SaveData();
 
         data.inventory = new InventoryItem[InventoryManager.Instance.inventorySize];
         for (int i = 0; i<InventoryManager.Instance.inventorySize; i++) {
             if(InventoryManager.Instance.inventory[i]!=null)
                 data.inventory[i]=InventoryManager.Instance.inventory[i];
         }
         bf.Serialize (file, data);
         file.Close();
         
     }
 }
 
 [Serializable]
 class SaveData{
     public InventoryItem[] inventory;
     //public Sprite[] inventory_sprites;
     //public Quest[] quests;
     public float[] playerPosition;
 }

Gives the following error:

 SerializationException: Type UnityEngine.ScriptableObject in assembly UnityEngine, Version=0.0.0.0, Culture=neutral, PublicKeyToken=null is not marked as serializable.

The InventoryItem class is set as [System.Serializable].