9:null 18:T51a,undefined For the system of equations AX = B: A non-singular matrix has determinant 0 and an inverse A^-1 exists. A singular matrix has determinant = 0 and no inverse exists.

When A is non-singular, the system has a unique solution. Since A^-1 exists, multiply both sides by A^-1: A^-1(AX) = A^-1B (A^-1A)X = A^-1B X = A^-1B This gives exactly one solution.

When A is singular, the system cannot have a unique solution. Since A^-1 does not exist, the system may have either infinitely many solutions or no solution at all, depending on B.

Checking Statement 1: "If A is singular, then AX = B has a unique solution." This is incorrect. A singular matrix cannot produce a unique solution.

Checking Statement 2: "If A is non-singular, then AX = B has infinitely many solutions." This is incorrect. A non-singular matrix produces exactly one solution X = A^-1B, not infinitely many.

Checking Statement 3: "If A is non-singular, then AX = B has a unique solution." This is correct. When A is non-singular, X = A^-1B gives a unique solution.

Checking Statement 4: "If A is singular, then AX = B is always consistent." This is incorrect. A singular matrix does not guarantee consistency; the system may have no solution depending on B.

Therefore, the correct answer is Option 3.19:T51a,undefined For the system of equations AX = B: A non-singular matrix has determinant 0 and an inverse A^-1 exists. A singular matrix has determinant = 0 and no inverse exists.

When A is non-singular, the system has a unique solution. Since A^-1 exists, multiply both sides by A^-1: A^-1(AX) = A^-1B (A^-1A)X = A^-1B X = A^-1B This gives exactly one solution.

When A is singular, the system cannot have a unique solution. Since A^-1 does not exist, the system may have either infinitely many solutions or no solution at all, depending on B.

Checking Statement 1: "If A is singular, then AX = B has a unique solution." This is incorrect. A singular matrix cannot produce a unique solution.

Checking Statement 2: "If A is non-singular, then AX = B has infinitely many solutions." This is incorrect. A non-singular matrix produces exactly one solution X = A^-1B, not infinitely many.

Checking Statement 3: "If A is non-singular, then AX = B has a unique solution." This is correct. When A is non-singular, X = A^-1B gives a unique solution.

Checking Statement 4: "If A is singular, then AX = B is always consistent." This is incorrect. A singular matrix does not guarantee consistency; the system may have no solution depending on B.

Therefore, the correct answer is Option 3.10:[["$","title","0",{"children":"CUET Mathematics - For the system of equations AX = B, which of the following is correct? | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"$18"}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$undefined"}],["$","meta","3",{"name":"keywords","content":"CUETMAT,MAT,Algebra,Matrices & Determinants"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","meta","5",{"name":"category","content":"education"}],["$","meta","6",{"name":"google-site-verification","content":"google"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - For the system of equations AX = B, which of the following is correct? | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"$19"}],"$L1a","$L1b","$L1c","$L1d","$L1e","$L1f","$L20","$L21","$L22","$L23","$L24","$L25","$L26","$L27","$L28","$L29","$L2a","$L2b"]

CUET Mathematics 2025 14 May Shift 2 PYQs

Keyboard Shortcuts