Question

Let A be an 4 × 3 matrix and supossed that the vectors z1 = ? 1 ? ? 1 ? ? 2 ? , z2 = ? 1 ? ? 0 ? ? -1 ? form a basis for N(A). If b = a1 + 2a2 + a3 ( where a1, a2, a3 are the columns of A), find all solutions of the system Ax = b. (Hint: Remember that the general solution of the equation Ax = b can be written as ? = x0 + c1x1 + c2x2 + ... + cnxn )

          Let A be an 4 × 3 matrix and supossed that the vectors

z1 = ? 1 ?
     ? 1 ?
     ? 2 ? , z2 = ?  1 ?
                    ?  0 ?
                    ? -1 ?

form a basis for N(A). If b = a1 + 2a2 + a3 ( where a1, a2, a3 are the columns of A), find all solutions of the system Ax = b.
(Hint: Remember that the general solution of the equation Ax = b can be written as ? = x0 + c1x1 + c2x2 + ... + cnxn )

Let A be an 4 × 3 matrix and supossed that the vectors

z1 = ? 1 ?
? 1 ?
? 2 ? , z2 = ? 1 ?
? 0 ?
? -1 ?

form a basis for N(A). If b = a1 + 2a2 + a3 ( where a1, a2, a3 are the columns of A), find all solutions of the system Ax = b.
(Hint: Remember that the general solution of the equation Ax = b can be written as ? = x0 + c1x1 + c2x2 + ... + cnxn )

Added by Joshua A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

04/26/2023

Step 1

We are given that Z1 and Z2 form a basis for N(A), which means they are linearly independent and any vector in N(A) can be written as a linear combination of Z1 and Z2. Show more…

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Let A be an 4 x 3 matrix and suppose that the vectors z1 = (1, 1, 2), z2 = (1, 0, -1) form a basis for N(A). If b = a1 + 2a2 + a3 (where a1, a2, a3 are the columns of A), find all solutions of the system Ax = b. (Hint: Remember that the general solution of the equation Ax = b can be written as ϕ = x0 + c1x1 + c2x2 + ... + cnxn )