Matthew, 47, from North Berwick, has played in eight Solheim Cups between 1998 and 2015, earning 19 points from 33 matches.
She was a member of three winning teams in 2003, 2011 and 2013.
She holed the winning putt in 2003 at Barseback Golf and Country Club in Sweden and secured the half-point to win the cup outright and seal Europe’s first away victory at Colorado Golf Club in 2013.
The USA are the holders of the Solheim Cup after winning 14½-13½ in Germany in 2015, a victory that gave them an overall lead of 9-5 in the event’s history.
BBC golf correspondent Iain Carter
Both captains have gone with their strongest pairings in what is set to be a huge opening match.
It is no surprise that Thompson and Kerr have been paired together and nor is Europe’s bullish combination of Reid and Hull. The top match can set momentum, but the bottom contest is often equally vital. Late replacement Matthew has therefore been given a huge responsibility.
The US intend using all 12 players on day one, but Europe’s Annika Sorenstam refused to say whether she would use the same tactic.
-9: M Every (US); -8: H Stenson (Swe); -7: V Taylor (US), C Smith (Aus), W Simpson (US), T Wilkinson (Aus), B Campbell (US), H Varner III (US); -6: D Love III (US), R Lamb (US), M Flores (US), S Saunders (US)
Selected others: -4: M Laird (Sco), R Knox (Sco), P Harrington (Ire); -3: S Lowry (Ire), S Power (Ire); -2: G Owen (Eng)
World number 751 Matt Every shot a nine-under-par round of 61 to lead Sweden’s Henrik Stenson by a shot after round one of the Wyndham Championship.
The American, 33, claimed the last of his two PGA Tour wins in 2015 but has missed the cut 20 times this season.
After holing from 105 yards for eagle on the first at Sedgefield Country Club in Greensboro, North Carolina, Every added seven more birdies.
He missed a 30ft birdie putt on the 18th hole to equal the course record.
“The last couple of years have been brutal for me,” said Every. “A lot of people probably would have quit so it’s good to be back, playing good. I’ve got a few things to motivate me right now and I want to play well again.”
Stenson, who has 15 wins across the PGA and European Tour including the 2016 Open Championship, carded a bogey-free 62. A sublime tee-shot on the par-three 16th to within three feet of the pin took him one shot behind Every.
A cluster of players including four-time PGA Tour winner Webb Simpson are a shot further back on seven under.
The American was seven under after just nine holes but cancelled out two birdies with two dropped shots on the back nine.
Scotland’s Martin Laird and Russell Knox are on four under. England’s Greg Owen is on two under, while Luke Donald – who was runner-up in the tournament in 2016 – made bogey on 18 to drop back to one under.
Rory McIlroy might not play again in 2017 as he continues to struggle with the rib injury which has limited him to 13 tournaments in a winless season.
McIlroy shot a closing 68 to end the US PGA on one over par, and has now gone three years without a major victory.
“I don’t know what I’m going to do,” said McIlroy, who suffered the injury testing equipment over the winter.
“You might not see me until next year. You might see me in a couple of weeks’ time. It really depends.”
McIlroy came into the US PGA as the pre-tournament favourite on the back of top-five finishes in his last two starts and a brilliant record at the host venue of Quail Hollow, including two wins and a course record of 61.
However, the 28-year-old was never in contention for a first major success since the 2014 US PGA at Valhalla and now faces the dilemma of whether to try and win the FedEx Cup – and the $10m bonus that comes with it – for the second year running.
“I can go out there and play and shoot decent scores, but when I come off the course I feel my left rhomboid going into spasm,” explained the Northern Irishman.
“The inside of my left arm goes numb. So I don’t know what to do. I have got this next week off to assess what I need to go forward.”
McIlroy began the week 43rd in the FedEx Cup rankings and needs to be in the top 30 to qualify for the season-ending Tour Championship in late September.
The play-offs get under way with the Northern Trust Open on 24 August and McIlroy is the defending champion of the Dell Technologies Championship the following week.
However, he already has one eye on next April’s Masters, which he needs to win to complete the career grand slam.
FedEx Cup dilemma
“I feel like I’m capable of playing well enough to give myself a chance in it,” McIlroy said of the FedEx Cup. “At the same time, April is a long way away. That’s the next big thing on my radar.
“I feel like I have a sense of, not duty, but I’ve missed a lot of time already. If I’m capable of playing, I feel like why shouldn’t you.
“But then at the same time if you are not capable of playing at your best, why should you play. It’s a Catch-22.”
McIlroy took six weeks off after losing out in a play-off for the South African Open in January and also missed the BMW PGA Championship at Wentworth and the Memorial Tournament.
“I felt like we took as much time as we needed to at the start of the year,” added McIlroy, who will seek the advice of sports scientist Steve McGregor in Northern Ireland in the next few days.
“It felt okay through the Masters and I switched it off for a couple of weeks because I was getting married, going on honeymoon. Then once I started practising again, I didn’t build up the volume gradually. I went from zero to hitting balls for three or four hours a day. That aggravated it a little bit.
“I just haven’t allowed it the time to fully heal. I wanted to play the season. I feel like I’m capable of playing well and winning and putting rounds together. If I want to challenge on a more consistent basis, I need to get 100 per cent healthy. I want to get back into that winner’s circle.”
Kisner’s consistency had seen him finish as co-leader in the opening two rounds and he continued that until a bogey on the 12th ended a run of 25 holes without dropping a shot.
He recovered with birdies on 14 and 15 to stretch his lead and move to 10 under.
But on 16 – the first of Quail Hollow’s fearsome closing stretch nicknamed the ‘Green Mile – he found the water and made double bogey.
That took the world number 25 back to eight under and briefly level with Stroud before the latter bogeyed the 17th moments later and did the same on 18.
Kisner made par on 17 but on the final hole hit his second shot into a stream only for it to fortunately bounce out and into the rough.
The American could only make bogey though which saw his lead cut back to one shot.
“I didn’t make the putts I’ve been making the first two days and had just a terrible finish there,” said Kisner.
“It feels easy until you smack one in the water and then it seems hard again.”
McIlroy and Spieth fade
The build-up to this year’s event was heavily focussed on McIlroy and Spieth with the Northern Ireland player favourite at Quail Hollow – where he holds the course record – and the American bidding to beat that record held by compatriot Woods.
Neither had threatened the top of the leaderboard in the opening rounds but day three was where their challenges ended.
McIlroy said he required “two 67s” to have a “really good chance” after finishing his first 36 holes on two over, but instead hit a two-over-par 73 which included five bogeys.
“It was sort of the same as the first couple of rounds,” McIlroy said. “I have been struggling to get anything going.”
Spieth played a better level-par round which included three consecutive birdies on the back nine before being spoiled by a double bogey six on the 18th hole.
Woods was aged 24 years, seven months and 25 days when he completed the full set of majors and Spieth will be older than that when he returns for the US PGA – the only major he is yet to win – when it moves to May in 2018.
“I didn’t have it written in a diary from when I was young that I need to win a career Grand Slam as the youngest ever. That wasn’t the goal,” Spieth said.
“The PGA Championship I think is going to be the toughest for me. I think I will play this tournament worse than the other three majors just in the way that it’s set up.”
US PGA Championship 2017
Venue: Quail Hollow, Charlotte Dates: 10-13 August
Coverage: Watch live on BBC Two, Red Button and BBC Sport website. Listen to BBC Radio 5 live commentary and follow text updates – including in-play video clips – on website and mobile app. Click for full times.