#symmetric matrix

Matrices and Determinants 3

If A = [ array*20c 1&3 + x&2 1 - x&2&y + 1 2&5 - y&3 array ] is a symmetric matrix, then 3x + y is equal to?

We can see that after simplifying, -1 is left. The method is simple: formula → substitution → calculation → answer.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

View Details

Matrices and Determinants 3

If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = [ array*20c 2&3 5& - 1 array ] , then AB i

We know that we verify [ array*20c 4& - 2 - 1& - 4 array ] by full calculation: use standard identity, substitute, simplify step by step to reach [ array*20c 4& - 2 - 1& - 4 array ].

Ref: NCERT Mathematics Class XII — Matrices and Determinants

View Details

Matrices and Determinants 2

If A = [ array*20c 2&3 - ;1&2 array ] = 1/2;( P + Q ) where P is symmetric and Q is skew symmetric matrix then P and Q a

Recall the rule formula P=A+Aᵀ gives symmetric, Q=A-Aᵀ gives skew. Computing: P=[[6,6,5],[6,2,9],[5,9,14]], Q=[[0,-2,5],[2,0,-3],[-5,3,0]]. Full solution.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

View Details

Matrices and Determinants 1

If A = [ array*20c 3&2&5 4&1&3 0&6&7 array ] = 1/2 (P + Q) where P is symmetric and Q is skew symmetric matrix then P an

Look at it this way: formula P=A+Aᵀ gives symmetric, Q=A-Aᵀ gives skew. Computing: P=[[6,6,5],[6,2,9],[5,9,14]], Q=[[0,-2,5],[2,0,-3],[-5,3,0]]. Full solution.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

View Details

Matrices and Determinants 1

If a matrix A is Symmetric as well as Skew-Symmetric, then:

The logic is straightforward: symmetric means A=Aᵀ, skew means A=-Aᵀ. So A=-A gives 2A=0, so A=0. Complete solution gives null matrix, all entries zero.

Ref: NCERT Mathematics Class XII — Matrices and Determinants

View Details