Title: MAT. Matrius. Operacions
Course: Matemàtiques de 3r d'ESO

Q: Sigui $$ A=\left( \begin{array}{ccc} x & {{a}}\\{{b}} & y\\ \end{array} \right) $$ . Trobeu els valors de les variables x i y perquè es compleixi que $$A^2=A$$
- $$x={=(1+sqrt(1-4*{a}*{b}))/2} y={=(1-sqrt(1-4*{a}*{b}))/2}$$
- $$x={=(1-sqrt(1-4*{a}*{b}))/2} y={=(1+sqrt(1-4*{a}*{b}))/2}$$
- $$x={=(1-sqrt(1-4*{a}*{b}))/2} y={=(1-sqrt(1-4*{a}*{b}))/2}$$
- $$x={=(1+sqrt(1-4*{a}*{b}))/2} y={=(1+sqrt(1-4*{a}*{b}))/2}$$
- $$x={=(1+sqrt(1-4*{a}*{b}))/2+1} y={=(1-sqrt(1-4*{a}*{b}))/2+1}$$
- $$x={=(1+sqrt(1-4*{a}*{b}))/2+1} y={=-(1-sqrt(1-4*{a}*{b}))/2-1+3}$$
- $$x={=-(1+sqrt(1-4*{a}*{b}))/2-1} y={=(1-sqrt(1-4*{a}*{b}))/2-3}$$
- $$x={=-(1+sqrt(1-4*{a}*{b}))/2-1} y={=-(1-sqrt(1-4*{a}*{b}))/2-2}$$
- $$x={=(1+sqrt(1-4*{a}*{b}))/2-1} y={=(1-sqrt(1-4*{a}*{b}))/2}$$
- $$x={=-(1+sqrt(1-4*{a}*{b}))/2+1} y={=-(1-sqrt(1-4*{a}*{b}))/2+2}$$
- $$x={=-(1+sqrt(1-4*{a}*{b}))/2+1} y={=(1-sqrt(1-4*{a}*{b}))/2}$$
- No té solució
- Una altra solució
A: $$x={=(1+sqrt(1-4*{a}*{b}))/2} y={=(1-sqrt(1-4*{a}*{b}))/2}$$ (formula; values not in the backup's text) / $$x={=(1-sqrt(1-4*{a}*{b}))/2} y={=(1+sqrt(1-4*{a}*{b}))/2}$$ (formula; values not in the backup's text)
If right: La teva resposta és correcta.
If partly right: La teva resposta és parcialment correcta.
If wrong: La teva resposta és incorrecta.

Q: $$ {\left( \begin{array}{ccc} \sqrt{{p}} & \sqrt{{q}}\\\sqrt{{q}} & \sqrt{{p}}\\ \end{array} \right)}^2 $$

Possibles respostes

A. $$ \left( \begin{array}{ccc} {{p}} & {{q}}\\{{q}} & {{p}}\\ \end{array} \right) $$

B. $$ \left( \begin{array}{ccc} {={p}-{q}} & {={p}-{q}}\\{={p}-{q}} & {={p}-{q}}\\ \end{array} \right) $$

C. $$ \left( \begin{array}{ccc} {=({p}-{q})*({p}-{q})}&{=({p}-{q})*({p}-{q})}\\{=({p}-{q})*({p}-{q})} & {=({p}-{q})*({p}-{q})}\\ \end{array} \right) $$

D. $$ \left( \begin{array}{ccc} {={p}+{q}} & 2\sqrt{{={p}*{q}}}\\2\sqrt{{={p}*{q}}} & {={p}+{q}}\\ \end{array} \right) $$

E. $$ \left( \begin{array}{ccc} 2\sqrt{{p}}+2\sqrt{{q}} & 2\sqrt{{p}}+2\sqrt{{q}}\\2\sqrt{{p}}+2\sqrt{{q}} & 2\sqrt{{p}}+2\sqrt{{q}}\\ \end{array} \right) $$
- A
- B
- C
- D
- E
- {={p}+{q}-{p}-{q}}
A: D
If right: La teva resposta és correcta.
If partly right: La teva resposta és parcialment correcta.
If wrong: La teva resposta és incorrecta.