Prime Minister Pierre Trudeau, who sought to bridge the historic gulf between the English and French part of Canada, was defeated in today's general election after 11 years in power.

Early returns and computer projections by major news organizations indicated a strong swing from Trudeau's Liberal Party except in overwhelmingly French-speaking Quebec.

Although the estimated 10 million voters endorsed a mandate for change. they did not give Conservative Party leader Joe Clark an absolute majority in the three-way race.

Clark now faces the difficult task of forming a minority government, and the balance of power in the new Parliament is likely to be held by Edward Broadbent and his socialist New Democratic Party.

A sad-looking Trudeau late tonight conceded defeat in a speech to Liberal campaign workers and said he will recommend that the governor general ask Clark to form a new government.

There were tears in the crowd as some partism supporters shouted, "Don't give up." Although his defeat marked the end of an era, Trudeau pledged that the Liberals are going to continue to fight for national unity.

"We took the risk and perhaps we failed in the short run, but I believe this is the course that Canada will have to follow," he said. "We have lost the campaign, but we will continue to fight for those principles."

A Canadian Broadcasting Corp. projection with more than half of the total vote counted dicicated that Clark's victory may not reach the magic number of 142 of the new Parliament's 282 seats. Projections by Canadian television confirmed this.

Tonight's results confirmed earlier projections of a very polarized Canada emerging as a result of Trudeau's Liberal's overwhelming strength in French Canada while English Canada was solidly behind Clark's Conservatives.

Ontario, which has one-third of Canada's 23 million citizens, was crucial for victory. In 1974, that English-speaking province elected 55 Liberals, 25 Conservatives and 8 New Democrats.

With results declared or projected in all 282 districts, the total for seats are:

Conservatives 137

Liberals 113

New Democrats 26

Others 6

Despite the clear Conservative lead, Trudeau's Liberals had a slight edge in the popular vote. Broadbent's New Democrats made strong inroads throughout the west.

Clark, 39, a University of Alberta graduate who has been involved in Conservative politics since his student days, would become the youngest prime minister in Canada's history. He entered Parliament six years ago, winning a seat from his native Alberta, and was elected party leader in 1977.

Clark, in his victory speech, pledged to form "a genuine national government" and to "modernize and remodel the Canadian confederation to fit the 1980s."

Then, in a gesture to French Canadians who voted overwhelmingly for his opponents, Clark said in French that Quebec citizens would enjoy full partnership in the new national government.

"Quebec will not be isolated in the Clark government," he said.

For Trudeau, this has been the hardest political fight of his life. He has been going against the public desire for change after 16 years of Liberal rule in a country beset by increasing provincial jealousies and distrust of Ottawa.

But the main issue underlying the two-month campaign was the critical question of national unity threatened by a strong separatist movement in the French-speaking Quebec.

Trudeau was seeking a fourth term as the Quebec issue is entering a decisive phase. It was his desire to dispel Quebec nationalism by making 6 million French Canadians fully accepted and integrated into Canada's national life that brought him into politics in the first place.

Quebec will decide in a referendum later this year whether it wants to be sovereign while remaining in an economic association with the rest of Canada. Trudeau has argued that Canada needs a strong federal leadership and that he was better equipped than his opponent to prevent a breakup of the country.

But apart from talking about new federalism, the Liberal leader's strategy was to link national unity to the issue of leadership. In an aggressively harsh and hard-hitting campaign, Trudeau sought to portary Clark, 39, as an incompetent and indecisive youth ill-equipped to lead the country.

Clark, who promised to put a "freash face" on federalism, largely ignored the Quebec issue. Instead, he focused on Canada's ailing economy with its 10 percent inflation, 9 percent unemployment, a declining dollar and a record balance of payments deficit of $4.6 billion since 1973.

In a clear appeal to the middle class, Clark also proposed making part of property taxes and home mortgage interest payments tax deductible. The Liberals, who adopted a similar measure for corporations and businesses only last year, were hurt by the Clark proposal.

While conceding privately that Quebec is the most difficult issue facing the next government, Clark talked of Canada as a "community of communities." He also expressed optimism that with the strong backing of English Canada he would be in a better position to reach an accommodation with Quebec.

Both Trudeau and Clark were aware that the stunning victory in 1976 of the separatist Parti Quebecois made this one of the crucial moments in modern Canadian history. They offered distinct choices.

Trudeau, a French Canadian from Montreal, in Quebec, argued that the Quebec residents must feel that they are represented in Ottawa if the struggle against separatism is to suceed. He suggested that the rift in the country along the language line would turn into a chasm if Clark won.

While many from Quebec may support the separatist cause, they were expected to give the great majority of Quebec's 75 seats to their native son.

On the other hand, Clark argued that Trudeau's policies over the past 11 years have left Canada more divided than ever. Clark, who has acquired fluency in French, believes that his concept of a new federation would be acceptable to all 10 provinces, including Quebec.

Trudeau voted this morning in his Montreal district and then returned to Ottawa to watch the returns on television at his official residence.

Clark voted in his Yellowhead district in Alberta where he will remain until Wednesday. Broadbent voted in Oshawa, his district near Toronto.

For Trudeau the reelection campaign was an unusually difficult one. The breakup of his marriage was followed by a winter of economic difficulties, and the approaching June deadline for calling elections. CAPTION: Picture 1, Prime Minister Trudeau, AP; Picture 2, challengers Ed Broadbent, UPI; Picture 3, Joe Clark vote in their home districts. UPI