If A is a square matrix of order 3 and |A| = 4, then |2A| equals
Notice that we verify 32 by full calculation: use standard identity, substitute, simplify step by step to reach 32.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
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The Inverse of the Matrix is Possible only for
The trick is after simplifying, Non-Singular Matrix is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
If the matrix A=bmatrix2-x&1&1 1&3-x&0 -1&-3&-xbmatrix is singular, then what is the solution set S?
Recall the rule after simplifying, S = 0, 2, 3 is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
If a, b, c are non-coplanar then find the value of 2[a b c] + [b a c] =
Here's the idea in simple terms: solving fully: apply relevant formula, put numbers, compute. Result comes as [a b c]. Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XII — Vectors and 3D Geometry
What is the minor, M₂₃ of bmatrix 0 & 4 & 6 -4 & 0&-2 -6& 2 & 0 bmatrix
Simply put, using formula we get 24. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get 24.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
If x y z are all different and not equal to zero and | array*20c 1 + x&1&1 1&1 + y&1 1&1&1 + z array | = 0 then the valu
Simply put, we verify -1 by full calculation: use standard identity, substitute, simplify step by step to reach -1.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
If A is an orthogonal matrix, then |A| is
In easy words, using formula we get +1. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get +1.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
If A=bmatrix 1& 3 5& 2bmatrix and B=bmatrix 3&2 1& 3bmatrix , then |AB| = ?
Applying the basic concept, using formula we get -91. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get -91.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
If A is a singular matrix, then A(adj A) is a / an
Look at it this way: using formula we get null matrix. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get null matrix.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
The given system of equations kx + 5y + 3z = 1, x + 3y + 2z = 3, x + 2y + z = 3 has no solution for -
The trick is complete solution: write formula, plug data, do arithmetic. Final value matches k = 2. Simple and accurate.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
If the system of equations px - 2y - pz = 0, 2x + py - pz = 0, -px + py + 2z = 0 has a non-trivial solution, then the su
In easy words, we verify 0 by full calculation: use standard identity, substitute, simplify step by step to reach 0.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
Consider the below statements - (i) For a matrix system AX = B, there will be a unique solution only iff |A| ≠ 0. (ii) A
Look at it this way: rule: unique iff |A|≠0. If |A|=0 and (adjA)B=0, you get infinite solutions. So i and iii correct. Full logic.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
