ArrayFilter mongo DB

I'm dealing with a mongo database and my table looks like this.
currently to update everything I use the save method passing it a bean but it doesn't work if I have to update only one element of the array as it overwrites the whole record.

{
"_id" : "21",
"idVlt" : "187",
"giochi" : [
    {
        "_id" : "22",
        "installed" : "true",
        "enable" : "true",
        "urlimg" : "placeholder.png",
        "categories" : [

        ],
        "tags" : [

        ]
    },
    {
        "_id" : "151",
        "installed" : "true",
        "enable" : "false",
        "urlimg" : "placeholder.png",
        "categories" : [

        ],
        "tags" : [

        ]
    },
    {
        "_id" : "197",
        "installed" : "true",
        "enable" : "false",
        "urlimg" : "placeholder.png",
        "categories" : [

        ],
        "tags" : [

        ]
    }
],

}

I would like to understand how I can update the element of the array with _id:22 : "installed":"true" --> false

and being able to insert a new element into the array :

 {
    "_id" : "222",
    "installed" : "true",
    "enable" : "true",
    "urlimg" : "placeholder.png",
    "categories" : [

    ],
    "tags" : [

    ]
}

with db.AssociazioneGameVlt.find({ $and: [ {"giochi._id":"77"}] })
i've

To update the element in the giochi array with the _id: "22" you can use the following update query:

db.collection.update({
  "_id": "21",
  "giochi._id": "22"
},
{
  $set: {
    "giochi.$.installed": "false"
  }
})

And to add a new element you can use below

db.collection.update(
   { "_id": "21" },
      { $push: { "giochi": {
          "_id" : "222",
          "installed" : "true",
          "enable" : "true",
          "urlimg" : "placeholder.png",
          "categories": [],
          "tags": []
        } }
      }
    )

Thanks, i try it on my mongodb and it's ok....
now i traslate it in code java like this

Query query = new Query(Criteria.where("idVlt").is("148"));
	  query.addCriteria(Criteria.where("giochi._id").is("197"));
	  System.out.println("query : "+query);
	  var update = Update.update("giochi.$.installed", "148_197");
	  System.out.println("update : "+update);
	  mongoTemplate.findAndModify(query, update,AssociazioneGameVlt.class );

But i've this error :
org.springframework.data.mongodb.UncategorizedMongoDbException: Command failed with error 2 (BadValue): 'The positional operator did not find the match needed from the query.' on server...

however, if I put '0' instead of '$' it modifies the first element of the array instead of getting the correct one