Find a basis for the column space ofA=⎡⎣⎢⎢−43820−4−2−34010⎤⎦⎥⎥.

Consider the matrixA=⎡⎣⎢12−1370251−2−42⎤⎦⎥.Find a basis for the column space of A. A.⎧⎩⎨⎪⎪⎡⎣⎢100⎤⎦⎥,⎡⎣⎢310⎤⎦⎥⎫⎭⎬⎪⎪ B.⎧⎩⎨⎪⎪⎡⎣⎢12−1⎤⎦⎥,⎡⎣⎢370⎤⎦⎥,⎡⎣⎢251⎤⎦⎥⎫⎭⎬⎪⎪ C.⎧⎩⎨⎪⎪⎡⎣⎢12−1⎤⎦⎥,⎡⎣⎢370⎤⎦⎥⎫⎭⎬⎪⎪ D.⎧⎩⎨⎪⎪⎡⎣⎢12−1⎤⎦⎥⎫⎭⎬⎪⎪

Find the basis for the kernel of the matrixA=⎛⎝⎜11−12−105−41001⎞⎠⎟A. {⎛⎝⎜⎜⎜1−311⎞⎠⎟⎟⎟} B. {⎛⎝⎜⎜⎜1−310⎞⎠⎟⎟⎟}C. {⎛⎝⎜⎜⎜1310⎞⎠⎟⎟⎟} D. {⎛⎝⎜⎜⎜−1310⎞⎠⎟⎟⎟}

If 𝑆 = {𝑣1 , 𝑣2, . . . , 𝑣𝑛 } is a set of vectors in a finite dimensional vector space 𝑉 , then 𝑆 is called a basis for 𝑉 if:

Find a basis for the row space and the rank of the matrix.−3 1 2 10 6 5−7 5 8(a) a basis for the row space

Write the standard basis for the vector space.R6