线性代数+概率论选择题刷题

q:"18. A是n阶方阵|A|=0，则A中()", opts:["A.必有一列全零","B.必有两列成比例","C.一列可由其余列线性表示","D.任一列可由其余表示"], ans:"C", desc:"行列式为0⇔列向量线性相关，至少一个向量可被其余表出" }, { q:"19. 向量β可由向量组A线性表示，则向量组B={A,β}的秩()A的秩", opts:["A.大于","B.等于","C.小于","D.无关"], ans:"B", desc:"新增可被表出的向量，秩不变" }, { q:"20. 非齐次Ax=B方程个数少于未知数，则()", opts:["A.Ax=B必无穷多解","B.Ax=0只有零解","C.Ax=0必有非零解","D.Ax=B必无解"], ans:"C", desc:"齐次方程组未知数多于方程，秩小于变量数，存在非零解" }, { q:"21. 非齐次Ax=B说法正确的是()", opts:["A.Ax=0只有零解→Ax=B无解","B.Ax=0有非零解→Ax=B有解","C.Ax=B有解→Ax=0非零解","D.Ax=B有唯一解→Ax=0只有零解"], ans:"D", desc:"唯一解说明r(A)=变量数，齐次只有零解" } ]; let current = 0; const qIndexEl = document.getElementById("qIndex"); const qTextEl = document.getElementById("qText"); const optBoxEl = document.getElementById("optBox"); const resultEl = document.getElementById("result"); const submitBtn = document.getElementById("submit"); const nextBtn = document.getElementById("next"); // 渲染当前题目 function render(){ const item = questionList[current]; qIndexEl.innerText = `第${current+1}题 / 共${questionList.length}题`; qTextEl.innerText = item.q; optBoxEl.innerHTML = ""; resultEl.style.display = "none"; // 生成单选选项 item.opts.forEach(opt=>{ const div = document.createElement("div"); div.className = "opt-item"; const radio = document.createElement("input"); radio.type = "radio"; radio.name = "quizOpt"; radio.value = opt[0]; const label = document.createElement("label"); label.innerText = opt; div.appendChild(radio); div.appendChild(label); optBoxEl.appendChild(div); }) } // 提交判题 submitBtn.onclick = function(){ const selected = document.querySelector('input[name="quizOpt"]:checked'); if(!selected){ alert("请选择一个选项！"); return; } const userAns = selected.value; const rightAns = questionList[current].ans; const desc = questionList[current].desc; resultEl.style.display = "block"; if(userAns === rightAns){ resultEl.className = "correct"; resultEl.innerHTML = `✅ 回答正确！
解析：${desc}
`; }else{ resultEl.className = "wrong"; resultEl.innerHTML = `❌ 回答错误，正确答案：${rightAns}
解析：${desc}
`; } } // 下一题 nextBtn.onclick = function(){ if(current < questionList.length - 1){ current++; render(); }else{ alert("已经是最后一题，刷题完成！"); } } // 初始化加载第一题 render();
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