If A=[1 2−1 3]B=[4 01 5]C=[2 01−2], a = 4, and b = - 2,

1.	If A=[1 2−1 3]B=[4 01 5]C=[2 01−2], a = 4, and b = - 2, then show that: (i) A + (B + C) = (A + B) + C (ii) A (BC) = (AB) C (iii) (a + b)B = aB + bB (iv) a (C - A) = aC - aA (v) (AT)T = A (vi) (bA)T = b AT (vii) (AB)T=BTAT (viii) (A - B)C = AC - BC (ix) (A−B)T=AT−BT
Answer» If $A = [\begin{matrix} 12 - 13 \end{matrix}] B = [\begin{matrix} 4015 \end{matrix}] C = [\begin{matrix} 20 1 - 2 \end{matrix}]$ , a = 4, and b = - 2, then show that: (i) A + (B + C) = (A + B) + C (ii) A (BC) = (AB) C (iii) (a + b)B = aB + bB (iv) a (C - A) = aC - aA (v) $(A^{T})^{T}$ = A (vi) $(b A)^{T}$ = b $A^{T}$ (vii) $(A B)^{T} = B^{T} A^{T}$ (viii) (A - B)C = AC - BC (ix) $(A - B)^{T} = A^{T} - B^{T}$

If A=[1 2−1 3]B=[4 01 5]C=[2 01−2], a = 4, and b = - 2, then show that: (i) A + (B + C) = (A + B) + C (ii) A (BC) = (AB) C (iii) (a + b)B = aB + bB (iv) a (C - A) = aC - aA (v) (AT)T = A (vi) (bA)T = b AT (vii) (AB)T=BTAT (viii) (A - B)C = AC - BC (ix) (A−B)T=AT−BT

Answer»

If $A = [\begin{matrix} 12 - 13 \end{matrix}] B = [\begin{matrix} 4015 \end{matrix}] C = [\begin{matrix} 20 1 - 2 \end{matrix}]$ ,
a = 4, and b = - 2, then show that:

(i) A + (B + C) = (A + B) + C

(ii) A (BC) = (AB) C

(iii) (a + b)B = aB + bB

(iv) a (C - A) = aC - aA

(v) $(A^{T})^{T}$ = A

(vi) $(b A)^{T}$ = b $A^{T}$

(vii) $(A B)^{T} = B^{T} A^{T}$

(viii) (A - B)C = AC - BC

(ix) $(A - B)^{T} = A^{T} - B^{T}$

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If A=[1 2−1 3]B=[4 01 5]C=[2 01−2], a = 4, and b = - 2, then show that: (i) A + (B + C) = (A + B) + C (ii) A (BC) = (AB) C (iii) (a + b)B = aB + bB (iv) a (C - A) = aC - aA (v) (AT)T = A (vi) (bA)T = b AT (vii) (AB)T=BTAT (viii) (A - B)C = AC - BC (ix) (A−B)T=AT−BT

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