Vector Parameter - Linear Algebra - Quiz Solution, Exercises of Linear Algebra

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Math 205 Quiz 2 Name: KEY 12 3 1A=]2 3 4 3.4 5 a) (a) Solve the equation Az = 0. Write the answer in vector parameter form. Av flort £1 = 3 V [e° 2 Na = -2xs t})-2] fr teR X3 free ! Y (b) Using (a), are the columns of A linearly independent or dependent? If they are dependent, find some ¢1,€2,¢3 (not all zero) such that c1@] + cada + e343 = M- 24,4 G7 40 Qt) C2772 —~d, +24, 7a, >) 2 B= [ A 5 P what a,b will the columns of B span R2? be az-h which sacl Atk ab except for ( Oo 20 } \ ‘| will nef span R™ for aélR atl off foros usil span 3. Build a matrix (choose numbers m and n and fill in the matrix) to demonstrate the following: 1p) (@) Anm by n matrix whose columns are linearly independent but do not span R™. \ oO 0 o-c Ly (b) An m by n matrix which spans R™ but whose columns are not linearly independent. 'o4 oO} |} 1