#transpose

Matrices and Determinants 3

If A, B are square matrices of the same order and B is a skew-symmetric matrix, then A′BA is:

We know that using formula we get Skew-Symmetric matrix.. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get Skew-Symmetric matrix..

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Matrices and Determinants 2

If A = [ array*20c 2θ & - 2θ 2θ & 2θ array ] and A + Aᵀ = I Where I is the unit matrix of 2 × 2 & Aᵀ is the transpose of

In easy words, after simplifying, 6 is left. The method is simple: formula → substitution → calculation → answer.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Matrices and Determinants 2

If ABᵀ is defined as a square matrix then what is the order of the matrix B, where matrix A has order 2 × 3.

We know that complete solution: write formula, plug data, do arithmetic. Final value matches 2 × 3. Simple and accurate.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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General Mathematics 1

If A = 13 ( array*20c 1&2&2 2&1&-2 -2&2&-1 array ) then (AAᵀ)-¹ = ?

Here's the idea in simple terms: complete solution: write formula, plug data, do arithmetic. Final value matches I. Simple and accurate.

Ref: NCERT Mathematics Class XI and XII

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Matrices and Determinants 1

A square matrix A is called orthogonal if_______ where A’ is the transpose of A.

Let's break it down: orthogonal definition: Aᵀ=A⁻¹. Then AAᵀ=I and AᵀA=I. Complete solution: transpose equals inverse preserves length.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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Matrices and Determinants 1

lf the order of A is 4 × 3, the order of B is 4 × 5 and the order of C is 7 × 3, then the order of (AᵀB)ᵀ C ᵀ is

The trick is Aᵀ is 3×4, so AᵀB is 3×5. Then (AᵀB)ᵀ is 5×3. Cᵀ is 3×7. Multiply 5×3 with 3×7 =5×7. Final order 5×7.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

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