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Which of the following statement are True.(1) if a matrix has n^2 entries , where n belongs to N , then it is a square matrix.

Is Cramer 's Rule applicable for solving the linear system below? If yes, apply it. Otherwise, alter the last equation in the system so that the solution can be obtained by applying the rule.

x+y+z=π

-πx +πy+ √2 z =0

π^2 x+ π^2 y+2z =0.

x+y+z=π

-πx +πy+ √2 z =0

π^2 x+ π^2 y+2z =0.

Give example, with justification , of the following: (1) two non -zero ,3×3 matrices A and B , with|A| =0, |B|= (5/7)i ; (2) . two non - singular 2×2 matrices C and D , with |C| = √2 |D| ?

If a and b are non-collinear vectors and A = (x+y)a + (2x + y+1)b. Find x and y

Find the inverse of the matrix A =[1 - 1 1, 1 - 2 4, 1 2 2] by gauss Jordan method.

Show that the inner product of the vectors

x ⃗=a_1 (e_1 ) ⃗+a_2 (e_2 ) ⃗+⋯.+a_n (e_n ) ⃗

And X ⃗=|■((e_1 ) ⃗&(e_2 ) ⃗@a_1&a_2 )|+|■((e_2 ) ⃗&(e_3 ) ⃗@a_2&a_3 )|+⋯+|■((e_n ) ⃗&(e_n ) ⃗@a_n&a_n )| vanishes.

x ⃗=a_1 (e_1 ) ⃗+a_2 (e_2 ) ⃗+⋯.+a_n (e_n ) ⃗

And X ⃗=|■((e_1 ) ⃗&(e_2 ) ⃗@a_1&a_2 )|+|■((e_2 ) ⃗&(e_3 ) ⃗@a_2&a_3 )|+⋯+|■((e_n ) ⃗&(e_n ) ⃗@a_n&a_n )| vanishes.

Find the basis of M2={(a,b,c,d):a,b,c,d ∈ R}

6x+18=h(3x+9)

Explain the meanings of the terms linearly dependent and coplanar. Make sure you demonstrate that you understand the difference between the terms, and the situation in which linear dependency implies coplanarity.

Suppose that a bike rents for $4 plus $ 1.50 per hours. write an equation in slope - intercept form that models this situation