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Australia climber's anguish at wife's Everest death
"I asked, 'Do you mind if I go on,' and she said, 'Yes, you go on, I'll wait for you here'," Mr Gropel, a Melbourne veterinarian, told Channel 7's Sunday Night programme.
"When I made it to the summit of Everest it wasn't special for me because I didn't have her there. I just ran up and down and it didn't mean anything to me."
The couple were both above 8,000m (26,000ft), an area known as the "death zone" because of the lack of oxygen.
Mr Gropel, who was also suffering from altitude sickness, said that although he knew his wife was ill, he thought she would be OK.
"She was feeling strong, she was walking, I mean she was short-roped because she was still quite weak, but she was walking fine, very slowly but fine. She was talking, I had her back and I don't know what happened," he said.
Mr Gropel said he still couldn't look at pictures of his wife "because it breaks my heart".
Sherpas brought Ms Strydom's body down the mountain on Wednesday from where it was airlifted to the Nepali capital, Kathmandu. Mr Gropel is also now in Kathmandu.
Ms Strydom, a lecturer at Monash University in Melbourne, was one of three climbers to die on Everest this month. Dutch climber Eric Ary Arnold died on Friday, 20 May, after reaching the summit and Indian climber Subhash Paul died the following Sunday as he descended the mountain.
Before setting off, Ms Strydom had said she and her husband, who is also a vegan, had been inspired to tackle Everest and the six other highest mountains on other continents after receiving questions about their diet.
"It seems that people have this warped idea of vegans being malnourished and weak," she said.
"By climbing the seven summits we want to prove that vegans can do anything and more."
Altitude sickness, also known as acute mountain sickness, occurs when people have difficulty adapting to low oxygen levels at high altitude.
Most cases are mild and result in headaches, nausea or dizziness, but in rare cases there can be a potentially fatal build-up of fluid on the brain and lungs.