Dynamically uncheck multiple select options in md-select angular 4.x

I am trying to implement on click of a button in mat-select multiple, an option should get unchecked and should be removed from the checked list too.

for removing the selected option I have written my code as below :

mat-select Option:

<mat-form-field class="full-width">
          <mat-select class="multiple-location-list-search-wrapper full-width" #mulLoc required placeholder="Locations" multiple>
            <mat-option *ngFor="let l of locationsBasedOnPropertyType; let i = index" class="multiple-field-box" [hidden]="tempLocations[i]"
              [value]="l">
              {{ l.value }}
            </mat-option>
          </mat-select>
        </mat-form-field>

Delete button:

<span (click)="deleteLocation(i, mulLoc);">Delete Location</span>
          <p>
            <strong>{{mulLoc.value[i].value}}</strong>
          </p>

Delete function:

  deleteLocation(index, multipleLocation){
    multipleLocation.selected[index]._selected = false;
    multipleLocation.selected[index]._active = false;
    multipleLocation.selected.splice(index,1);
    multipleLocation.value.splice(index,1);
  }

By Implementing above, I am able to delete option from selected & value array but it's not reflecting in Material UI. Location option is not getting unchecked.

Is there any Hack or internal Method to do the same?

Thanks in advance!

@Will Howel, Thanks for your help man.

But I got my solution Like below:

I did some research in
'..app-folder../node_modules/@angular/material/select/typings/select.d.ts'
I found
writeValue(value: any): void;

The changes I made in my view :

<mat-select class="full-width" #mulLoc required placeholder="Locations" multiple [(ngModel)]="resLoc" name="resLoc">
    <mat-option *ngFor="let l of locations; let i = index [hidden]="tempLocations[i]" [value]="l">
{{ l.value }}
</mat-option>
</mat-select>

Objects :

locations = [
{id : 'IND',value : 'india'},
{id : 'INS',value : 'indonesia'},
{id : 'THL',value : 'thailand'}
]
resLoc = [locations[0], locations[2]]

Component : this is the function which I am calling for deleting(unselecting) location

deleteLocation(i,mulLoc) {
    this.resLoc.splice(i,1); // my ngModel
    mulLoc.writeValue(this.resLoc); // reference variable of mat-select
  }

Hope it helps! happy coding!